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<!-- DFIN ActiveDisclosure(SM) XBRL Linkbase Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2022-02-02T05:15:14.7751442+00:00 -->
<!-- Version            : 5.0.1.728 -->
<!-- Package ID         : d98eafcefde34e5b8faaf981270ba6bd -->
<!-- Copyright (c) 2022 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel" xlink:type="simple" />
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  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://fasb.org/us-gaap/role/label/axisDefault" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-roles-2021-01-31.xsd#axisDefault" xlink:type="simple" />
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityCentralIndexKey" xlink:type="locator" xlink:label="dei_EntityCentralIndexKey" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_SegmentProfitLoss" xlink:type="locator" xlink:label="ufi_SegmentProfitLoss" />
    <link:label xml:lang="en-US" xlink:label="ufi_SegmentProfitLoss_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Aggregate revenue earned or expenditure incurred less cost of goods and services sold or operating expenses directly attributable to the revenue generation activity plus depreciation expense.</link:label>
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    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_CoverAbstract" xlink:type="locator" xlink:label="dei_CoverAbstract" />
    <link:label xml:lang="en-US" xlink:label="dei_CoverAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
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    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityRegistrantName" xlink:type="locator" xlink:label="dei_EntityRegistrantName" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityRegistrantName_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityRegistrantName_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
    <link:label xml:lang="en-US" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityFileNumber" xlink:type="locator" xlink:label="dei_EntityFileNumber" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityFileNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityFileNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityTaxIdentificationNumber" xlink:type="locator" xlink:label="dei_EntityTaxIdentificationNumber" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_TradingSymbol" xlink:type="locator" xlink:label="dei_TradingSymbol" />
    <link:label xml:lang="en-US" xlink:label="dei_TradingSymbol_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_TradingSymbol" xlink:to="dei_TradingSymbol_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_TradingSymbol_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityIncorporationStateCountryCode" xlink:type="locator" xlink:label="dei_EntityIncorporationStateCountryCode" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation State Country Code</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_CurrentFiscalYearEndDate" xlink:type="locator" xlink:label="dei_CurrentFiscalYearEndDate" />
    <link:label xml:lang="en-US" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CurrentFiscalYearEndDate" xlink:to="dei_CurrentFiscalYearEndDate_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityFilerCategory" xlink:type="locator" xlink:label="dei_EntityFilerCategory" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityFilerCategory_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Filer Category</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFilerCategory" xlink:to="dei_EntityFilerCategory_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityFilerCategory_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityCommonStockSharesOutstanding" xlink:type="locator" xlink:label="dei_EntityCommonStockSharesOutstanding" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding (in shares)</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCommonStockSharesOutstanding" xlink:to="dei_EntityCommonStockSharesOutstanding_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock Shares Outstanding</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_DocumentType" xlink:type="locator" xlink:label="dei_DocumentType" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentType_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentType_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_DocumentPeriodEndDate" xlink:type="locator" xlink:label="dei_DocumentPeriodEndDate" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentPeriodEndDate" xlink:to="dei_DocumentPeriodEndDate_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_DocumentFiscalYearFocus" xlink:type="locator" xlink:label="dei_DocumentFiscalYearFocus" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Document Fiscal Year Focus</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalYearFocus" xlink:to="dei_DocumentFiscalYearFocus_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_DocumentFiscalPeriodFocus" xlink:type="locator" xlink:label="dei_DocumentFiscalPeriodFocus" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalPeriodFocus" xlink:to="dei_DocumentFiscalPeriodFocus_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_AmendmentFlag" xlink:type="locator" xlink:label="dei_AmendmentFlag" />
    <link:label xml:lang="en-US" xlink:label="dei_AmendmentFlag_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_AmendmentFlag_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityCurrentReportingStatus" xlink:type="locator" xlink:label="dei_EntityCurrentReportingStatus" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCurrentReportingStatus" xlink:to="dei_EntityCurrentReportingStatus_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityInteractiveDataCurrent" xlink:type="locator" xlink:label="dei_EntityInteractiveDataCurrent" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Interactive Data Current</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityInteractiveDataCurrent" xlink:to="dei_EntityInteractiveDataCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntitySmallBusiness" xlink:type="locator" xlink:label="dei_EntitySmallBusiness" />
    <link:label xml:lang="en-US" xlink:label="dei_EntitySmallBusiness_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntitySmallBusiness" xlink:to="dei_EntitySmallBusiness_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntitySmallBusiness_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityEmergingGrowthCompany" xlink:type="locator" xlink:label="dei_EntityEmergingGrowthCompany" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Emerging Growth Company</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityShellCompany" xlink:type="locator" xlink:label="dei_EntityShellCompany" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityShellCompany_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityShellCompany" xlink:to="dei_EntityShellCompany_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityShellCompany_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_Security12bTitle" xlink:type="locator" xlink:label="dei_Security12bTitle" />
    <link:label xml:lang="en-US" xlink:label="dei_Security12bTitle_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12bTitle" xlink:to="dei_Security12bTitle_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_Security12bTitle_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Security12b Title</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_SecurityExchangeName" xlink:type="locator" xlink:label="dei_SecurityExchangeName" />
    <link:label xml:lang="en-US" xlink:label="dei_SecurityExchangeName_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SecurityExchangeName" xlink:to="dei_SecurityExchangeName_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_SecurityExchangeName_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityAddressAddressLine1" xlink:type="locator" xlink:label="dei_EntityAddressAddressLine1" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address Address Line1</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityAddressCityOrTown" xlink:type="locator" xlink:label="dei_EntityAddressCityOrTown" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address City Or Town</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityAddressStateOrProvince" xlink:type="locator" xlink:label="dei_EntityAddressStateOrProvince" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address State Or Province</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_ReceivablesNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Receivables, net</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherAssetsCurrent" xlink:type="locator" xlink:label="us-gaap_OtherAssetsCurrent" />
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    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AssetsCurrent" xlink:type="locator" xlink:label="us-gaap_AssetsCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options exercised (in shares)</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Stock Options Exercised</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of restricted stock units</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross" xlink:to="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Value Restricted Stock Award Gross</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of restricted stock units (in shares)</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Restricted Stock Award Gross</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="locator" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments To Additional Paid In Capital Sharebased Compensation Requisite Service Period Recognition Value</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation (in shares)</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Share Based Compensation</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:type="locator" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock repurchased and retired under publicly announced program</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased And Retired During Period Value</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:type="locator" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock repurchased and retired under publicly announced program (in shares)</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:to="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased And Retired During Period Shares</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="locator" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock withheld in satisfaction of tax withholding obligations under net share settle transactions</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments Related To Tax Withholding For Share Based Compensation</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:type="locator" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock withheld in satisfaction of tax withholding obligations under net share settle transactions (in shares)</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:to="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Shares Paid For Tax Withholding For Share Based Compensation</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income (loss), net of tax</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProfitLoss" xlink:type="locator" xlink:label="us-gaap_ProfitLoss" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProfitLoss_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProfitLoss" xlink:to="us-gaap_ProfitLoss_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProfitLoss_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Profit Loss</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance (in shares)</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities" xlink:type="locator" xlink:label="ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities" />
    <link:label xml:lang="en-US" xlink:label="ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The increase (decrease) during the reporting period in the accounts payable and other current liabilities.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities" xlink:to="ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram" xlink:type="locator" xlink:label="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram" />
    <link:label xml:lang="en-US" xlink:label="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments for Common stock repurchased and retired under publicly announced program.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram" xlink:to="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementOfCashFlowsAbstract" xlink:type="locator" xlink:label="us-gaap_StatementOfCashFlowsAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Statement Of Cash Flows [Abstract]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating activities:</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Operating Activities [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="locator" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net income to net cash (used) provided by operating activities:</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments To Reconcile Net Income Loss To Cash Provided By Used In Operating Activities [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:type="locator" xlink:label="us-gaap_DepreciationDepletionAndAmortization" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization expense</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation Depletion And Amortization</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash" xlink:type="locator" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash compensation expense</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash" xlink:to="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Employee Benefits And Share Based Compensation Noncash</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInDeferredIncomeTaxes" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInDeferredIncomeTaxes" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInDeferredIncomeTaxes_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deferred income taxes</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherNoncashIncomeExpense" xlink:type="locator" xlink:label="us-gaap_OtherNoncashIncomeExpense" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNoncashIncomeExpense" xlink:to="us-gaap_OtherNoncashIncomeExpense_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncash Income Expense</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in assets and liabilities:</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Operating Capital [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInReceivables" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInReceivables" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInReceivables_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Receivables, net</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInReceivables_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Receivables</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInInventories" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInInventories" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Inventories</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Inventories</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other current assets</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:to="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" />
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInIncomeTaxes" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInIncomeTaxes" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInIncomeTaxes_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income taxes</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInIncomeTaxes" xlink:to="us-gaap_IncreaseDecreaseInIncomeTaxes_lbl" />
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    <link:label xml:lang="en-US" xlink:label="ufi_IncreaseDecreaseInAccountsPayableAndOtherCurrentLiabilities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable and other current liabilities</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet" xlink:to="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssetsAndLiabilitiesNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Other Noncurrent Assets And Liabilities Net</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash (used) provided by operating activities</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Operating Activities</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Investing Activities [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Capital expenditures</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Payments To Acquire Property Plant And Equipment</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsToAcquireIntangibleAssets" xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of intangible asset</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireIntangibleAssets" xlink:to="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Payments To Acquire Intangible Assets</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="locator" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Payments For Proceeds From Other Investing Activities</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used by investing activities</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Investing Activities</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Financing Activities [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProceedsFromLinesOfCredit" xlink:type="locator" xlink:label="us-gaap_ProceedsFromLinesOfCredit" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromLinesOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from ABL Revolver</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromLinesOfCredit" xlink:to="us-gaap_ProceedsFromLinesOfCredit_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromLinesOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Lines Of Credit</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RepaymentsOfLinesOfCredit" xlink:type="locator" xlink:label="us-gaap_RepaymentsOfLinesOfCredit" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments on ABL Revolver</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfLinesOfCredit" xlink:to="us-gaap_RepaymentsOfLinesOfCredit_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Repayments Of Lines Of Credit</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RepaymentsOfSecuredDebt" xlink:type="locator" xlink:label="us-gaap_RepaymentsOfSecuredDebt" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RepaymentsOfSecuredDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments on ABL Term Loan</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfSecuredDebt" xlink:to="us-gaap_RepaymentsOfSecuredDebt_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RepaymentsOfSecuredDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Repayments Of Secured Debt</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProceedsFromConstructionLoansPayable" xlink:type="locator" xlink:label="us-gaap_ProceedsFromConstructionLoansPayable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromConstructionLoansPayable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from construction financing</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromConstructionLoansPayable" xlink:to="us-gaap_ProceedsFromConstructionLoansPayable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromConstructionLoansPayable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Construction Loans Payable</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FinanceLeasePrincipalPayments" xlink:type="locator" xlink:label="us-gaap_FinanceLeasePrincipalPayments" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments on finance lease obligations</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeasePrincipalPayments" xlink:to="us-gaap_FinanceLeasePrincipalPayments_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Principal Payments</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock repurchased and retired under publicly announced program</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PaymentsForCommonStockRepurchasedAndRetiredUnderPubliclyAnnouncedProgram_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Payments For Common Stock Repurchased And Retired Under Publicly Announced Program</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="locator" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Payments For Other Financing Activities</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used by financing activities</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided By Used In Financing Activities</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:type="locator" xlink:label="us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" />
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    <link:label xml:lang="en-US" xlink:label="us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Effect Of Exchange Rate On Cash And Cash Equivalents</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" />
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    <link:label xml:lang="en-US" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_NatureOfOperations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Background</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_NatureOfOperations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Nature Of Operations</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:type="locator" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" />
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    <link:loc xlink:href="ufi-20211226.xsd#ufi_StockBasedCompensationGrantedOrIssuedTableTextBlock" xlink:type="locator" xlink:label="ufi_StockBasedCompensationGrantedOrIssuedTableTextBlock" />
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    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ServiceMember" xlink:to="us-gaap_ServiceMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ServiceMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Service [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_REPREVEFiberMember" xlink:type="locator" xlink:label="ufi_REPREVEFiberMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_REPREVEFiberMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">REPREVE fiber.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_REPREVEFiberMember" xlink:to="ufi_REPREVEFiberMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_REPREVEFiberMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">REPREVE Fiber [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_REPREVEFiberMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">R E P R E V E Fiber [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_AllOtherProductsAndServicesMember" xlink:type="locator" xlink:label="ufi_AllOtherProductsAndServicesMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_AllOtherProductsAndServicesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">All other products and services.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_AllOtherProductsAndServicesMember" xlink:to="ufi_AllOtherProductsAndServicesMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_AllOtherProductsAndServicesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">All Other Products and Services [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_AllOtherProductsAndServicesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">All Other Products And Services [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:type="locator" xlink:label="us-gaap_DisaggregationOfRevenueLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Disaggregation Of Revenue [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueLineItems" xlink:to="us-gaap_DisaggregationOfRevenueLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation Of Revenue [Line Items]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ReservesForQualityClaims" xlink:type="locator" xlink:label="ufi_ReservesForQualityClaims" />
    <link:label xml:lang="en-US" xlink:label="ufi_ReservesForQualityClaims_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Reserves for quality claims.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ReservesForQualityClaims" xlink:to="ufi_ReservesForQualityClaims_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccountsReceivableGrossCurrent" xlink:type="locator" xlink:label="us-gaap_AccountsReceivableGrossCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer receivables</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGrossCurrent" xlink:to="us-gaap_AccountsReceivableGrossCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable Gross Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="locator" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Allowance for uncollectible accounts</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Allowance For Doubtful Accounts Receivable Current</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ReservesForQualityClaims_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Reserves for quality claims</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ReservesForQualityClaims_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Reserves For Quality Claims</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:type="locator" xlink:label="us-gaap_AccountsReceivableNetCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net customer receivables</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable Net Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherReceivables" xlink:type="locator" xlink:label="us-gaap_OtherReceivables" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherReceivables_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other receivables</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivables" xlink:to="us-gaap_OtherReceivables_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherReceivables_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Receivables</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_ReceivablesNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total receivables, net</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Accounts Notes Loans And Financing Receivable [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Accounts Notes Loans And Financing Receivable [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementBusinessSegmentsAxis" xlink:type="locator" xlink:label="us-gaap_StatementBusinessSegmentsAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segments</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Statement Business Segments [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SegmentDomain" xlink:type="locator" xlink:label="us-gaap_SegmentDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segments</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Segment [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_AsiaSegmentMember" xlink:type="locator" xlink:label="ufi_AsiaSegmentMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_AsiaSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Asia segment.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_AsiaSegmentMember" xlink:to="ufi_AsiaSegmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_AsiaSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asia [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_AsiaSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Asia Segment [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InvestmentTypeAxis" xlink:type="locator" xlink:label="us-gaap_InvestmentTypeAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InvestmentTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentTypeAxis" xlink:to="us-gaap_InvestmentTypeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InvestmentTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Investment Type [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:type="locator" xlink:label="us-gaap_InvestmentTypeCategorizationMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InvestmentTypeCategorizationMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentTypeCategorizationMember" xlink:to="us-gaap_InvestmentTypeCategorizationMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InvestmentTypeCategorizationMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Investment Type Categorization [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BankersAcceptanceMember" xlink:type="locator" xlink:label="us-gaap_BankersAcceptanceMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BankersAcceptanceMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Banker&apos;s Acceptance Notes [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BankersAcceptanceMember" xlink:to="us-gaap_BankersAcceptanceMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BankersAcceptanceMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Bankers Acceptance [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:type="locator" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Notes And Loans Receivable [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Notes And Loans Receivable [Line Items]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_NetRealizableValueAdjustment" xlink:type="locator" xlink:label="ufi_NetRealizableValueAdjustment" />
    <link:label xml:lang="en-US" xlink:label="ufi_NetRealizableValueAdjustment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Net realizable value adjustment.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_NetRealizableValueAdjustment" xlink:to="ufi_NetRealizableValueAdjustment_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InventoryRawMaterials" xlink:type="locator" xlink:label="us-gaap_InventoryRawMaterials" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryRawMaterials_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Raw materials</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryRawMaterials" xlink:to="us-gaap_InventoryRawMaterials_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryRawMaterials_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Raw Materials</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherInventorySupplies" xlink:type="locator" xlink:label="us-gaap_OtherInventorySupplies" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherInventorySupplies_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplies</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherInventorySupplies" xlink:to="us-gaap_OtherInventorySupplies_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherInventorySupplies_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Inventory Supplies</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InventoryWorkInProcess" xlink:type="locator" xlink:label="us-gaap_InventoryWorkInProcess" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryWorkInProcess_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Work in process</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryWorkInProcess" xlink:to="us-gaap_InventoryWorkInProcess_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryWorkInProcess_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Work In Process</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InventoryFinishedGoods" xlink:type="locator" xlink:label="us-gaap_InventoryFinishedGoods" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finished goods</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoods" xlink:to="us-gaap_InventoryFinishedGoods_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Finished Goods</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InventoryGross" xlink:type="locator" xlink:label="us-gaap_InventoryGross" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross inventories</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryGross" xlink:to="us-gaap_InventoryGross_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Gross</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NetRealizableValueAdjustment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net realizable value adjustment</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NetRealizableValueAdjustment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Realizable Value Adjustment</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_InventoryNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total inventories</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_RecoveryOfNonIncomeTaxesCurrentAsset" xlink:type="locator" xlink:label="ufi_RecoveryOfNonIncomeTaxesCurrentAsset" />
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Recovery of non income taxes current asset.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_RecoveryOfNonIncomeTaxesCurrentAsset" xlink:to="ufi_RecoveryOfNonIncomeTaxesCurrentAsset_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DepositsAssetsCurrent" xlink:type="locator" xlink:label="us-gaap_DepositsAssetsCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DepositsAssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vendor deposits</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepositsAssetsCurrent" xlink:to="us-gaap_DepositsAssetsCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DepositsAssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Deposits Assets Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ValueAddedTaxReceivableCurrent" xlink:type="locator" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Value-added taxes receivable</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ValueAddedTaxReceivableCurrent" xlink:to="us-gaap_ValueAddedTaxReceivableCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Value Added Tax Receivable Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherPrepaidExpenseCurrent" xlink:type="locator" xlink:label="us-gaap_OtherPrepaidExpenseCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherPrepaidExpenseCurrent" xlink:to="us-gaap_OtherPrepaidExpenseCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Prepaid Expense Current</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recovery of non-income taxes</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Recovery Of Non Income Taxes Current Asset</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ContractWithCustomerAssetNetCurrent" xlink:type="locator" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contract assets</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetNetCurrent" xlink:to="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Contract With Customer Asset Net Current</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other current assets</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ClaimRecoveryPeriod" xlink:type="locator" xlink:label="ufi_ClaimRecoveryPeriod" />
    <link:label xml:lang="en-US" xlink:label="ufi_ClaimRecoveryPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Claim recovery period.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ClaimRecoveryPeriod" xlink:to="ufi_ClaimRecoveryPeriod_lbl" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_LegalEntityAxis" xlink:type="locator" xlink:label="dei_LegalEntityAxis" />
    <link:label xml:lang="en-US" xlink:label="dei_LegalEntityAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal Entity</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LegalEntityAxis" xlink:to="dei_LegalEntityAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_LegalEntityAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Legal Entity [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2021/dei-2021.xsd#dei_EntityDomain" xlink:type="locator" xlink:label="dei_EntityDomain" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityDomain" xlink:to="dei_EntityDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="dei_EntityDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Entity [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ClaimRecoveryPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Claim recovery period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ClaimRecoveryPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Claim Recovery Period</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FinanceLeasesAccumulatedAmortization" xlink:type="locator" xlink:label="ufi_FinanceLeasesAccumulatedAmortization" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeasesAccumulatedAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Less: accumulated amortization &#8211; finance leases.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FinanceLeasesAccumulatedAmortization" xlink:to="ufi_FinanceLeasesAccumulatedAmortization_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Property Plant And Equipment [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Property Plant And Equipment [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Property Plant And Equipment By Type [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Property Plant And Equipment Type [Domain]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LandMember" xlink:type="locator" xlink:label="us-gaap_LandMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LandMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Land [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandMember" xlink:to="us-gaap_LandMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LandMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Land [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LandImprovementsMember" xlink:type="locator" xlink:label="us-gaap_LandImprovementsMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LandImprovementsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Land Improvements [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandImprovementsMember" xlink:to="us-gaap_LandImprovementsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LandImprovementsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Land Improvements [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BuildingAndBuildingImprovementsMember" xlink:type="locator" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Buildings and Improvements [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="us-gaap_BuildingAndBuildingImprovementsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Building And Building Improvements [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_AssetsHeldUnderFinanceLeasesMember" xlink:type="locator" xlink:label="ufi_AssetsHeldUnderFinanceLeasesMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_AssetsHeldUnderFinanceLeasesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Assets under Finance Leases.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_AssetsHeldUnderFinanceLeasesMember" xlink:to="ufi_AssetsHeldUnderFinanceLeasesMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_AssetsHeldUnderFinanceLeasesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets under Finance Leases [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_AssetsHeldUnderFinanceLeasesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Assets Held Under Finance Leases [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_MachineryAndEquipmentMember" xlink:type="locator" xlink:label="us-gaap_MachineryAndEquipmentMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Machinery and Equipment [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MachineryAndEquipmentMember" xlink:to="us-gaap_MachineryAndEquipmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Machinery And Equipment [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ComputersSoftwareAndOfficeEquipmentMember" xlink:type="locator" xlink:label="ufi_ComputersSoftwareAndOfficeEquipmentMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_ComputersSoftwareAndOfficeEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Computers, software and office equipment [member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ComputersSoftwareAndOfficeEquipmentMember" xlink:to="ufi_ComputersSoftwareAndOfficeEquipmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_ComputersSoftwareAndOfficeEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computers, Software and Office Equipment [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ComputersSoftwareAndOfficeEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Computers Software And Office Equipment [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_TransportationEquipmentMember" xlink:type="locator" xlink:label="us-gaap_TransportationEquipmentMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_TransportationEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transportation Equipment [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TransportationEquipmentMember" xlink:to="us-gaap_TransportationEquipmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_TransportationEquipmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Transportation Equipment [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AssetUnderConstructionMember" xlink:type="locator" xlink:label="us-gaap_AssetUnderConstructionMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetUnderConstructionMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction in Progress [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetUnderConstructionMember" xlink:to="us-gaap_AssetUnderConstructionMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetUnderConstructionMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Asset Under Construction [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property Plant And Equipment [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Property Plant And Equipment [Line Items]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentGross" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross PP&amp;E</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentGross" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Property Plant And Equipment Gross</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="locator" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: accumulated depreciation</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation Depletion And Amortization Property Plant And Equipment</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeasesAccumulatedAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: accumulated amortization &#8211; finance leases</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeasesAccumulatedAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Leases Accumulated Amortization</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total PP&amp;E, net</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset" xlink:type="locator" xlink:label="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset" />
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Recovery of non income taxes non current asset.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset" xlink:to="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract" xlink:type="locator" xlink:label="ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract" />
    <link:label xml:lang="en-US" xlink:label="ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Disclosure - Other Non Current Assets - Schedule of Other Non-Current Assets (Details) [Abstract]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract" xlink:to="ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_DisclosureOtherNonCurrentAssetsScheduleOfOtherNonCurrentAssetsDetailsAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Disclosure Other Non Current Assets Schedule Of Other Non Current Assets Details [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recovery of non-income taxes</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_RecoveryOfNonIncomeTaxesNonCurrentAsset_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Recovery Of Non Income Taxes Non Current Asset</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" />
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    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments in unconsolidated affiliates</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DepositsAssetsNoncurrent" xlink:type="locator" xlink:label="us-gaap_DepositsAssetsNoncurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vendor deposits and other</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepositsAssetsNoncurrent" xlink:to="us-gaap_DepositsAssetsNoncurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Deposits Assets Noncurrent</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other non-current assets</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_UnconsolidatedEntitiesNumber" xlink:type="locator" xlink:label="ufi_UnconsolidatedEntitiesNumber" />
    <link:label xml:lang="en-US" xlink:label="ufi_UnconsolidatedEntitiesNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The number of unconsolidated entities that the company invests into.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_UnconsolidatedEntitiesNumber" xlink:to="ufi_UnconsolidatedEntitiesNumber_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investments And Joint Ventures [Abstract]</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Equity Method Investments [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Equity Method Investments [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="locator" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" />
    <link:label xml:lang="en-US" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment, Name</link:label>
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    <link:label xml:lang="en-US" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Equity Method Investment Equity Method Investee Name [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_EquityMethodInvesteeNameDomain" xlink:type="locator" xlink:label="srt_EquityMethodInvesteeNameDomain" />
    <link:label xml:lang="en-US" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment, Name</link:label>
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    <link:label xml:lang="en-US" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investee Name [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_UNFAndUNFAmericaMember" xlink:type="locator" xlink:label="ufi_UNFAndUNFAmericaMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAndUNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">UNF and UNF America.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_UNFAndUNFAmericaMember" xlink:to="ufi_UNFAndUNFAmericaMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAndUNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">UNF and UNF America [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAndUNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">U N F And U N F America [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="locator" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Equity Method Investments [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Equity Method Investments [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UnconsolidatedEntitiesNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unconsolidated Entities, Number</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UnconsolidatedEntitiesNumber_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Unconsolidated Entities Number</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted" xlink:type="locator" xlink:label="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase commitment, remaining minimum amount committed</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted" xlink:to="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Commitment Remaining Minimum Amount Committed</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_UNFAmericaMember" xlink:type="locator" xlink:label="ufi_UNFAmericaMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">UNF America.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_UNFAmericaMember" xlink:to="ufi_UNFAmericaMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">UNF America [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UNFAmericaMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">U N F America [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_UNFMember" xlink:type="locator" xlink:label="ufi_UNFMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">UNF.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_UNFMember" xlink:to="ufi_UNFMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_UNFMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">UNF [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UNFMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">U N F [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Raw material purchases under supply agreement</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty" xlink:to="us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction Purchases From Related Party</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent" xlink:type="locator" xlink:label="us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable, related parties</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent" xlink:to="us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsPayableRelatedPartiesCurrentAndNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable Related Parties Current And Noncurrent</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments" xlink:type="locator" xlink:label="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments" />
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of assets and liabilities accounted for by equity method investments.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments" xlink:to="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of current and total assets and total liabilities counted for by equity method investments</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfAssetsAndLiabilitiesAccountedForByEquityMethodInvestments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Assets And Liabilities Accounted For By Equity Method Investments</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Method Investment, Nonconsolidated Investee</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment Nonconsolidated Investee [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Method Investment, Nonconsolidated Investee</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment Nonconsolidated Investee [Domain]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Method Investment, Nonconsolidated Investee or Group of Investees</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment Nonconsolidated Investee Or Group Of Investees [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AssetsNoncurrent" xlink:type="locator" xlink:label="us-gaap_AssetsNoncurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetsNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-current assets</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNoncurrent" xlink:to="us-gaap_AssetsNoncurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AssetsNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Assets Noncurrent</link:label>
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    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LiabilitiesNoncurrent" xlink:type="locator" xlink:label="us-gaap_LiabilitiesNoncurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LiabilitiesNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-current liabilities</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesNoncurrent" xlink:to="us-gaap_LiabilitiesNoncurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LiabilitiesNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities Noncurrent</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shareholders&#8217; equity and capital accounts</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RetainedEarningsUndistributedEarningsFromEquityMethodInvestees" xlink:type="locator" xlink:label="us-gaap_RetainedEarningsUndistributedEarningsFromEquityMethodInvestees" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RetainedEarningsUndistributedEarningsFromEquityMethodInvestees_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">UNIFI&#8217;s portion of undistributed earnings</link:label>
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    <link:label xml:lang="en-US" xlink:label="us-gaap_RetainedEarningsUndistributedEarningsFromEquityMethodInvestees_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings Undistributed Earnings From Equity Method Investees</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization" xlink:type="locator" xlink:label="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization" />
    <link:label xml:lang="en-US" xlink:label="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The amount of the depreciation and amortization reported by an equity method investment of the entity.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization" xlink:to="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_Revenues" xlink:type="locator" xlink:label="us-gaap_Revenues" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_Revenues_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net sales</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_Revenues_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_Revenues_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Revenues</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_GrossProfit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross profit</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:type="locator" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Loss) income from operations</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Income Loss From Continuing Operations Including Portion Attributable To Noncontrolling Interest</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_EquityMethodInvestmentSummarizedFinancialInformationDepreciationAndAmortization_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment Summarized Financial Information Depreciation And Amortization</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Distributions received</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:to="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment Dividends Or Distributions</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_IncentiveCompensation" xlink:type="locator" xlink:label="ufi_IncentiveCompensation" />
    <link:label xml:lang="en-US" xlink:label="ufi_IncentiveCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Incentive Compensation.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_IncentiveCompensation" xlink:to="ufi_IncentiveCompensation_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="locator" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payroll and fringe benefits</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Employee Related Liabilities Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DeferredRevenueCurrent" xlink:type="locator" xlink:label="us-gaap_DeferredRevenueCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredRevenueCurrent" xlink:to="us-gaap_DeferredRevenueCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue Current</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_IncentiveCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incentive compensation</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_IncentiveCompensation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Incentive Compensation</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent" xlink:type="locator" xlink:label="us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of supplemental post-employment plan</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent" xlink:to="us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PensionAndOtherPostretirementAndPostemploymentBenefitPlansLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Pension And Other Postretirement And Postemployment Benefit Plans Liabilities Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DerivativeLiabilitiesCurrent" xlink:type="locator" xlink:label="us-gaap_DerivativeLiabilitiesCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesCurrent" xlink:to="us-gaap_DerivativeLiabilitiesCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liabilities Current</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="locator" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities Current</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_DebtInstrumentMaturityMonthYear" xlink:type="locator" xlink:label="ufi_DebtInstrumentMaturityMonthYear" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentMaturityMonthYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument maturity month year.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_DebtInstrumentMaturityMonthYear" xlink:to="ufi_DebtInstrumentMaturityMonthYear_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentTable" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentTable" xlink:to="us-gaap_DebtInstrumentTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentAxis" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentNameDomain" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentNameDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Name</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Name [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ABLRevolverMember" xlink:type="locator" xlink:label="ufi_ABLRevolverMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLRevolverMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">ABL revolver.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ABLRevolverMember" xlink:to="ufi_ABLRevolverMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLRevolverMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABL Revolver [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ABLRevolverMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">A B L Revolver [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ABLTermLoanMember" xlink:type="locator" xlink:label="ufi_ABLTermLoanMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLTermLoanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">ABL term loan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ABLTermLoanMember" xlink:to="ufi_ABLTermLoanMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLTermLoanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABL Term Loan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ABLTermLoanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">A B L Term Loan [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongtermDebtTypeAxis" xlink:type="locator" xlink:label="us-gaap_LongtermDebtTypeAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeAxis" xlink:to="us-gaap_LongtermDebtTypeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Longterm Debt Type [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongtermDebtTypeDomain" xlink:type="locator" xlink:label="us-gaap_LongtermDebtTypeDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeDomain" xlink:to="us-gaap_LongtermDebtTypeDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Longterm Debt Type [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FinanceLeaseObligationsMember" xlink:type="locator" xlink:label="ufi_FinanceLeaseObligationsMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease obligations.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FinanceLeaseObligationsMember" xlink:to="ufi_FinanceLeaseObligationsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease Obligations [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Obligations [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ConstructionFinancingMember" xlink:type="locator" xlink:label="ufi_ConstructionFinancingMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_ConstructionFinancingMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Refers to information regarding long-term debt focusing on financing the company&apos;s construction endeavors.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ConstructionFinancingMember" xlink:to="ufi_ConstructionFinancingMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_ConstructionFinancingMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction Financing [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ConstructionFinancingMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Construction Financing [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentLineItems" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentLineItems" xlink:to="us-gaap_DebtInstrumentLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentMaturityMonthYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Maturity Date</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentMaturityMonthYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Maturity Month Year</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Interest Rate Effective Percentage</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap" xlink:type="locator" xlink:label="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective interest rate for the funds borrowed under the debt agreement considering interest compounding and original issue discount or premium including the effects of an interest rate swap.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap" xlink:to="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtNstrumentInterestRateEffectivePercentageIncludingTheEffectsOfAnInterestRateSwap_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Nstrument Interest Rate Effective Percentage Including The Effects Of An Interest Rate Swap</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FinancingObligationCurrentPortion" xlink:type="locator" xlink:label="ufi_FinancingObligationCurrentPortion" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinancingObligationCurrentPortion_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease pass-through financing obligation, current portion.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FinancingObligationCurrentPortion" xlink:to="ufi_FinancingObligationCurrentPortion_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FinanceLeaseLiability" xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiability" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease obligations</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiability" xlink:to="us-gaap_FinanceLeaseLiability_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Liability</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongTermDebt" xlink:type="locator" xlink:label="us-gaap_LongTermDebt" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction financing</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtAndCapitalLeaseObligations" xlink:type="locator" xlink:label="us-gaap_DebtAndCapitalLeaseObligations" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtAndCapitalLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtAndCapitalLeaseObligations" xlink:to="us-gaap_DebtAndCapitalLeaseObligations_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtAndCapitalLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt And Capital Lease Obligations</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SecuredDebtCurrent" xlink:type="locator" xlink:label="us-gaap_SecuredDebtCurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredDebtCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current ABL Term Loan</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredDebtCurrent" xlink:to="us-gaap_SecuredDebtCurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredDebtCurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Secured Debt Current</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinancingObligationCurrentPortion_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current portion of finance lease obligations</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinancingObligationCurrentPortion_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Financing Obligation Current Portion</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_UnamortizedDebtIssuanceExpense" xlink:type="locator" xlink:label="us-gaap_UnamortizedDebtIssuanceExpense" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_UnamortizedDebtIssuanceExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unamortized debt issuance costs</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnamortizedDebtIssuanceExpense" xlink:to="us-gaap_UnamortizedDebtIssuanceExpense_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_UnamortizedDebtIssuanceExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Unamortized Debt Issuance Expense</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebtAndCapitalLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total long-term debt</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LineOfCredit" xlink:type="locator" xlink:label="us-gaap_LineOfCredit" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LineOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCredit" xlink:to="us-gaap_LineOfCredit_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LineOfCredit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SecuredDebt" xlink:type="locator" xlink:label="us-gaap_SecuredDebt" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding balances of term loan</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredDebt" xlink:to="us-gaap_SecuredDebt_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Secured Debt</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FinanceLeaseObligationsRangeStartMonthAndYear" xlink:type="locator" xlink:label="ufi_FinanceLeaseObligationsRangeStartMonthAndYear" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeStartMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease obligations range start month and year.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FinanceLeaseObligationsRangeStartMonthAndYear" xlink:to="ufi_FinanceLeaseObligationsRangeStartMonthAndYear_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FinanceLeaseObligationsRangeEndMonthAndYear" xlink:type="locator" xlink:label="ufi_FinanceLeaseObligationsRangeEndMonthAndYear" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeEndMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease obligations range end month and year.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FinanceLeaseObligationsRangeEndMonthAndYear" xlink:to="ufi_FinanceLeaseObligationsRangeEndMonthAndYear_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeStartMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease obligations, scheduled maturity start date</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeStartMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Obligations Range Start Month And Year</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeEndMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease obligations, scheduled maturity end date</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FinanceLeaseObligationsRangeEndMonthAndYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Obligations Range End Month And Year</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_DebtAgreementMaximumBorrowingCapacity" xlink:type="locator" xlink:label="ufi_DebtAgreementMaximumBorrowingCapacity" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtAgreementMaximumBorrowingCapacity_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Maximum borrowing capacity under a debt agreement on the amount that could be borrowed with a combination of, but not limited to, a line of credit and term loan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_DebtAgreementMaximumBorrowingCapacity" xlink:to="ufi_DebtAgreementMaximumBorrowingCapacity_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ABLFacilityMember" xlink:type="locator" xlink:label="ufi_ABLFacilityMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLFacilityMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">ABL facility.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ABLFacilityMember" xlink:to="ufi_ABLFacilityMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_ABLFacilityMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABL Facility [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ABLFacilityMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">A B L Facility [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_TypeOfArrangementAxis" xlink:type="locator" xlink:label="us-gaap_TypeOfArrangementAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TypeOfArrangementAxis" xlink:to="us-gaap_TypeOfArrangementAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Type Of Arrangement [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:type="locator" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Arrangements And Nonarrangement Transactions [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_CreditAgreementMember" xlink:type="locator" xlink:label="ufi_CreditAgreementMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_CreditAgreementMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit agreement.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_CreditAgreementMember" xlink:to="ufi_CreditAgreementMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_CreditAgreementMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agreement [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_CreditAgreementMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agreement [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CreditFacilityAxis" xlink:type="locator" xlink:label="us-gaap_CreditFacilityAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityAxis" xlink:to="us-gaap_CreditFacilityAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CreditFacilityDomain" xlink:type="locator" xlink:label="us-gaap_CreditFacilityDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityDomain" xlink:to="us-gaap_CreditFacilityDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RevolvingCreditFacilityMember" xlink:type="locator" xlink:label="us-gaap_RevolvingCreditFacilityMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Facility [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevolvingCreditFacilityMember" xlink:to="us-gaap_RevolvingCreditFacilityMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_RangeAxis" xlink:type="locator" xlink:label="srt_RangeAxis" />
    <link:label xml:lang="en-US" xlink:label="srt_RangeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="srt_RangeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Range [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_RangeMember" xlink:type="locator" xlink:label="srt_RangeMember" />
    <link:label xml:lang="en-US" xlink:label="srt_RangeMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="srt_RangeMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Range [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_MaximumMember" xlink:type="locator" xlink:label="srt_MaximumMember" />
    <link:label xml:lang="en-US" xlink:label="srt_MaximumMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="srt_MaximumMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_MinimumMember" xlink:type="locator" xlink:label="srt_MinimumMember" />
    <link:label xml:lang="en-US" xlink:label="srt_MinimumMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="srt_MinimumMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_VariableRateAxis" xlink:type="locator" xlink:label="us-gaap_VariableRateAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateAxis" xlink:to="us-gaap_VariableRateAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_VariableRateDomain" xlink:type="locator" xlink:label="us-gaap_VariableRateDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateDomain" xlink:to="us-gaap_VariableRateDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LondonInterbankOfferedRateLIBORMember" xlink:type="locator" xlink:label="us-gaap_LondonInterbankOfferedRateLIBORMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LondonInterbankOfferedRateLIBORMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LIBOR [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LondonInterbankOfferedRateLIBORMember" xlink:to="us-gaap_LondonInterbankOfferedRateLIBORMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LondonInterbankOfferedRateLIBORMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">London Interbank Offered Rate L I B O R [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BaseRateMember" xlink:type="locator" xlink:label="us-gaap_BaseRateMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BaseRateMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Base Rate [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BaseRateMember" xlink:to="us-gaap_BaseRateMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_BaseRateMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Base Rate [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DerivativeInstrumentRiskAxis" xlink:type="locator" xlink:label="us-gaap_DerivativeInstrumentRiskAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Instrument</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentRiskAxis" xlink:to="us-gaap_DerivativeInstrumentRiskAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument Risk [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DerivativeContractTypeDomain" xlink:type="locator" xlink:label="us-gaap_DerivativeContractTypeDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Contract</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeContractTypeDomain" xlink:to="us-gaap_DerivativeContractTypeDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract Type [Domain]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InterestRateSwapMember" xlink:type="locator" xlink:label="us-gaap_InterestRateSwapMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateSwapMember" xlink:to="us-gaap_InterestRateSwapMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:type="locator" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SOFR [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:to="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate Sofr Overnight Index Swap Rate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtAgreementMaximumBorrowingCapacity_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt agreement maximum borrowing capacity</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtAgreementMaximumBorrowingCapacity_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Agreement Maximum Borrowing Capacity</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="locator" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, maximum borrowing capacity</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility Maximum Borrowing Capacity</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_SecuredDebt_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Principal amount of term loan</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentMaturityDate" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentMaturityDate" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument maturity date</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentMaturityDate" xlink:to="us-gaap_DebtInstrumentMaturityDate_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Maturity Date</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, basis spread on variable rate</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Basis Spread On Variable Rate1</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_NumberOfInterestRateSwaps" xlink:type="locator" xlink:label="ufi_NumberOfInterestRateSwaps" />
    <link:label xml:lang="en-US" xlink:label="ufi_NumberOfInterestRateSwaps_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of interest rate swaps.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_NumberOfInterestRateSwaps" xlink:to="ufi_NumberOfInterestRateSwaps_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_InterestRateSwapsTerminationPeriod" xlink:type="locator" xlink:label="ufi_InterestRateSwapsTerminationPeriod" />
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapsTerminationPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest rate swaps termination period.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_InterestRateSwapsTerminationPeriod" xlink:to="ufi_InterestRateSwapsTerminationPeriod_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_InterestRateSwapDeDesignated" xlink:type="locator" xlink:label="ufi_InterestRateSwapDeDesignated" />
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapDeDesignated_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest rate swap de-designated.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_InterestRateSwapDeDesignated" xlink:to="ufi_InterestRateSwapDeDesignated_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_NumberOfInterestRateSwaps_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of interest rate swaps</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NumberOfInterestRateSwaps_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Interest Rate Swaps</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DerivativeAverageFixedInterestRate" xlink:type="locator" xlink:label="us-gaap_DerivativeAverageFixedInterestRate" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeAverageFixedInterestRate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, average fixed interest rate</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAverageFixedInterestRate" xlink:to="us-gaap_DerivativeAverageFixedInterestRate_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeAverageFixedInterestRate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Average Fixed Interest Rate</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DerivativeNotionalAmount" xlink:type="locator" xlink:label="us-gaap_DerivativeNotionalAmount" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, notional amount</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNotionalAmount" xlink:to="us-gaap_DerivativeNotionalAmount_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Notional Amount</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapsTerminationPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps termination period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapsTerminationPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swaps Termination Period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapDeDesignated_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swap de-designated</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_InterestRateSwapDeDesignated_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap De Designated</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_DebtInstrumentNumberOfMonthlyPayments" xlink:type="locator" xlink:label="ufi_DebtInstrumentNumberOfMonthlyPayments" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentNumberOfMonthlyPayments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument, number of monthly payments.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_DebtInstrumentNumberOfMonthlyPayments" xlink:to="ufi_DebtInstrumentNumberOfMonthlyPayments_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations" xlink:type="locator" xlink:label="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations" />
    <link:label xml:lang="en-US" xlink:label="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term debt including transitioned amount of completed asset costs to finance lease obligations.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations" xlink:to="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_CompletedAssetCostTransferredToFinanceLeaseObligation" xlink:type="locator" xlink:label="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation" />
    <link:label xml:lang="en-US" xlink:label="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Completed asset cost transferred to finance lease obligation.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation" xlink:to="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentNumberOfMonthlyPayments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Monthly payment</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_DebtInstrumentNumberOfMonthlyPayments_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Number Of Monthly Payments</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate during period</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:to="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Interest Rate During Period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long term debt including transitioned amount</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_LongTermDebtIncludingTransitionedAmountOfCompletedAssetCostsToFinanceLeaseObligations_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt Including Transitioned Amount Of Completed Asset Costs To Finance Lease Obligations</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Completed asset cost transferred to finance lease obligation</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_CompletedAssetCostTransferredToFinanceLeaseObligation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Completed Asset Cost Transferred To Finance Lease Obligation</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour" xlink:type="locator" xlink:label="ufi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour" />
    <link:label xml:lang="en-US" xlink:label="ufi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term debt maturities repayments of principal after year four.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour" xlink:to="ufi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentRedemptionTable" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentRedemptionTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentRedemptionTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument Redemption [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionTable" xlink:to="us-gaap_DebtInstrumentRedemptionTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentRedemptionTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Redemption [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentRedemptionLineItems" xlink:type="locator" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument Redemption [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionLineItems" xlink:to="us-gaap_DebtInstrumentRedemptionLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Redemption [Line Items]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2022</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt Maturities Repayments Of Principal Remainder Of Fiscal Year</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2023</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt Maturities Repayments Of Principal In Next Twelve Months</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" />
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    <link:loc xlink:href="ufi-20211226.xsd#ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare" xlink:type="locator" xlink:label="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock repurchased and retired during period, average price paid per share.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare" xlink:to="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms" xlink:type="locator" xlink:label="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms" />
    <link:label xml:lang="en-US" xlink:label="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Approximate value that may yet be repurchased under the Plans or programs.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms" xlink:to="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_StockholdersEquityLineItems" xlink:type="locator" xlink:label="ufi_StockholdersEquityLineItems" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Stockholders equity.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_StockholdersEquityLineItems" xlink:to="ufi_StockholdersEquityLineItems_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_StockholdersEquityTable" xlink:type="locator" xlink:label="ufi_StockholdersEquityTable" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Stockholders equity.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_StockholdersEquityTable" xlink:to="ufi_StockholdersEquityTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders Equity [Table]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders Equity [Table]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PeriodAxis" xlink:type="locator" xlink:label="ufi_PeriodAxis" />
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Period.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_PeriodAxis" xlink:to="ufi_PeriodAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Period [Axis]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PeriodDomain" xlink:type="locator" xlink:label="ufi_PeriodDomain" />
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Period.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_PeriodDomain" xlink:to="ufi_PeriodDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Period</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PeriodDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Period [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FiscalYearThousandAndNineteenMember" xlink:type="locator" xlink:label="ufi_FiscalYearThousandAndNineteenMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearThousandAndNineteenMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Fiscal 2019.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FiscalYearThousandAndNineteenMember" xlink:to="ufi_FiscalYearThousandAndNineteenMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearThousandAndNineteenMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2019 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearThousandAndNineteenMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fiscal Year Thousand And Nineteen [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FiscalYearTwoThousandAndTwentyMember" xlink:type="locator" xlink:label="ufi_FiscalYearTwoThousandAndTwentyMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Fiscal 2020.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FiscalYearTwoThousandAndTwentyMember" xlink:to="ufi_FiscalYearTwoThousandAndTwentyMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2020 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fiscal Year Two Thousand And Twenty [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FiscalYearTwoThousandAndTwentyTwoMember" xlink:type="locator" xlink:label="ufi_FiscalYearTwoThousandAndTwentyTwoMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyTwoMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Fiscal 2022.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FiscalYearTwoThousandAndTwentyTwoMember" xlink:to="ufi_FiscalYearTwoThousandAndTwentyTwoMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyTwoMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2022 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyTwoMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fiscal Year Two Thousand And Twenty Two [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FiscalYearTwoThousandAndTwentyOneMember" xlink:type="locator" xlink:label="ufi_FiscalYearTwoThousandAndTwentyOneMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyOneMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Fiscal year two thousand and twenty one.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FiscalYearTwoThousandAndTwentyOneMember" xlink:to="ufi_FiscalYearTwoThousandAndTwentyOneMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyOneMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fiscal 2021 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FiscalYearTwoThousandAndTwentyOneMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fiscal Year Two Thousand And Twenty One [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders Equity [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockholdersEquityLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders Equity [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Number of Shares Repurchased as Part of Publicly Announced Plans or Programs</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Average Price Paid per Share</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockRepurchasedAndRetiredDuringPeriodAveragePricePaidPerShare_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased And Retired During Period Average Price Paid Per Share</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Approximate Dollar Value that May Yet Be Repurchased Under Publicly Announced Plans or Programs</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ApproximateValueThatMayYetBeRepurchasedUnderThePlansOrPrograms_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Approximate Value That May Yet Be Repurchased Under The Plans Or Programs</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate" xlink:type="locator" xlink:label="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate" />
    <link:label xml:lang="en-US" xlink:label="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award effective date.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate" xlink:to="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract" xlink:type="locator" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Employee Service Share Based Compensation Aggregate Disclosures [Abstract]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PlanNameAxis" xlink:type="locator" xlink:label="us-gaap_PlanNameAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PlanNameDomain" xlink:type="locator" xlink:label="us-gaap_PlanNameDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_The2013IncentiveCompensationPlanMember" xlink:type="locator" xlink:label="ufi_The2013IncentiveCompensationPlanMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_The2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The 2013 incentive compensation plan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_The2013IncentiveCompensationPlanMember" xlink:to="ufi_The2013IncentiveCompensationPlanMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_The2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">The 2013 Incentive Compensation Plan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_The2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">The2013 Incentive Compensation Plan [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember" xlink:type="locator" xlink:label="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The amended and restated 2013 incentive compensation plan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember" xlink:to="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">The Amended and Restated 2013 Incentive Compensation Plan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_TheAmendedAndRestated2013IncentiveCompensationPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">The Amended And Restated2013 Incentive Compensation Plan [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_TwoThousandTwentyPlanMember" xlink:type="locator" xlink:label="ufi_TwoThousandTwentyPlanMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_TwoThousandTwentyPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty plan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_TwoThousandTwentyPlanMember" xlink:to="ufi_TwoThousandTwentyPlanMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_TwoThousandTwentyPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2020 Plan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_TwoThousandTwentyPlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Plan [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_EmployeeStockPurchasePlanMember" xlink:type="locator" xlink:label="ufi_EmployeeStockPurchasePlanMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockPurchasePlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee Stock Purchase Plan.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_EmployeeStockPurchasePlanMember" xlink:to="ufi_EmployeeStockPurchasePlanMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockPurchasePlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Stock Purchase Plan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockPurchasePlanMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Purchase Plan [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective date</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEffectiveDate_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Effective Date</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of shares available for future issuance</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Number Of Shares Available For Grant</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AwardTypeAxis" xlink:type="locator" xlink:label="us-gaap_AwardTypeAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AwardTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardTypeAxis" xlink:to="us-gaap_AwardTypeAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AwardTypeAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Award Type [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award Type</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Award Type And Plan Name [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember" xlink:type="locator" xlink:label="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Awards expired, forfeited or otherwise terminated unexercised.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember" xlink:to="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Awards Expired, Forfeited or Otherwise Terminated Unexercised [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsExpiredForfeitedOrOtherwiseTerminatedUnexercisedMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Awards Expired Forfeited Or Otherwise Terminated Unexercised [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember" xlink:type="locator" xlink:label="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee stock option and restricted stock units issued to key employees.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember" xlink:to="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Awards Granted to Employees [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_EmployeeStockOptionAndRestrictedStockUnitsIssuedToKeyEmployeesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Option And Restricted Stock Units Issued To Key Employees [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_AwardsGrantedToNonEmployeeDirectorsMember" xlink:type="locator" xlink:label="ufi_AwardsGrantedToNonEmployeeDirectorsMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsGrantedToNonEmployeeDirectorsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Awards granted to non employee directors.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_AwardsGrantedToNonEmployeeDirectorsMember" xlink:to="ufi_AwardsGrantedToNonEmployeeDirectorsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsGrantedToNonEmployeeDirectorsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Awards Granted to Non-Employee Directors [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_AwardsGrantedToNonEmployeeDirectorsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Awards Granted To Non Employee Directors [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/positiveLabel">Authorized under the 2020 Plan</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Number Of Shares Authorized</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plus: Awards expired, forfeited or otherwise terminated unexercised</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Forfeitures And Expirations In Period</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Awards granted to employees</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Shares Issued In Period</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Awards granted to non-employee directors</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Grants In Period</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/positiveLabel">Available for issuance under the 2020 Plan</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_StockOptionsMember" xlink:type="locator" xlink:label="ufi_StockOptionsMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockOptionsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock options.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_StockOptionsMember" xlink:to="ufi_StockOptionsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_StockOptionsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock Options [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_StockOptionsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Stock Options [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RestrictedStockUnitsRSUMember" xlink:type="locator" xlink:label="us-gaap_RestrictedStockUnitsRSUMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockUnitsRSUMember" xlink:to="us-gaap_RestrictedStockUnitsRSUMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units R S U [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PerformanceSharesMember" xlink:type="locator" xlink:label="us-gaap_PerformanceSharesMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance Share Units [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PerformanceSharesMember" xlink:to="us-gaap_PerformanceSharesMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Performance Shares [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Grants In Period Gross</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted/Performance/Vested stock units</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PercentageOfDiscountFromMarketValue" xlink:type="locator" xlink:label="ufi_PercentageOfDiscountFromMarketValue" />
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfDiscountFromMarketValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of discount from market value.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_PercentageOfDiscountFromMarketValue" xlink:to="ufi_PercentageOfDiscountFromMarketValue_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:type="locator" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares reserved</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Capital Shares Reserved For Future Issuance</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfDiscountFromMarketValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of discount from market value</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PercentageOfDiscountFromMarketValue_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Discount From Market Value</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_ImpactOfInterestRateSwapsOnInterestExpense" xlink:type="locator" xlink:label="ufi_ImpactOfInterestRateSwapsOnInterestExpense" />
    <link:label xml:lang="en-US" xlink:label="ufi_ImpactOfInterestRateSwapsOnInterestExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Impact of interest rate swaps on interest expense.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_ImpactOfInterestRateSwapsOnInterestExpense" xlink:to="ufi_ImpactOfInterestRateSwapsOnInterestExpense_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1" xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in fair value of interest rate swaps</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1" xlink:to="us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncreaseDecreaseInFairValueOfInterestRateFairValueHedgingInstruments1_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Fair Value Of Interest Rate Fair Value Hedging Instruments1</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ImpactOfInterestRateSwapsOnInterestExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impact of interest rate swaps to increase interest expense</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_ImpactOfInterestRateSwapsOnInterestExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Impact Of Interest Rate Swaps On Interest Expense</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount" xlink:type="locator" xlink:label="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount" />
    <link:label xml:lang="en-US" xlink:label="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair value assets and liabilities transfers among level 1 level 2 and level 3 amount.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount" xlink:to="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="locator" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="locator" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value assets and liabilities amount transfers into or out of the levels</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_FairValueAssetsAndLiabilitiesTransfersAmongLevel1Level2AndLevel3Amount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Assets And Liabilities Transfers Among Level1 Level2 And Level3 Amount</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="locator" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income Loss [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income Loss [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="locator" xlink:label="us-gaap_AccumulatedTranslationAdjustmentMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedTranslationAdjustmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Currency Translation Adjustments [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="us-gaap_AccumulatedTranslationAdjustmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedTranslationAdjustmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Translation Adjustment [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:type="locator" xlink:label="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in Interest Rate Swaps [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:to="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Gain Loss Net Cash Flow Hedge Parent [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="locator" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income Loss [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income Loss [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other comprehensive (loss) income</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions" xlink:type="locator" xlink:label="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions" />
    <link:label xml:lang="en-US" xlink:label="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of unvested options that vest upon achievement of certain market conditions.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions" xlink:to="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic weighted average shares</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number Of Shares Outstanding Basic</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="locator" xlink:label="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net potential common share equivalents</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Incremental Common Shares Attributable To Share Based Payment Arrangements</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Diluted weighted average shares</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number Of Diluted Shares Outstanding</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract" xlink:type="locator" xlink:label="us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Excluded from the calculation of common share equivalents:</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract" xlink:to="us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_EarningsPerShareDilutedOtherDisclosuresAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share Diluted Other Disclosures [Abstract]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="locator" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Anti-dilutive common share equivalents (in shares)</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded From Computation Of Earnings Per Share Amount</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unvested stock options that vest upon achievement of certain market conditions (in shares)</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_UnvestedStockOptionsThatVestUponAchievementOfCertainMarketConditions_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Unvested Stock Options That Vest Upon Achievement Of Certain Market Conditions</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_NetMonitoringAndReportingCostsReveived" xlink:type="locator" xlink:label="ufi_NetMonitoringAndReportingCostsReveived" />
    <link:label xml:lang="en-US" xlink:label="ufi_NetMonitoringAndReportingCostsReveived_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Net monitoring and reporting costs reveived.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_NetMonitoringAndReportingCostsReveived" xlink:to="ufi_NetMonitoringAndReportingCostsReveived_lbl" />
    <link:loc xlink:href="ufi-20211226.xsd#ufi_TheTermOfAFormerGroundLease" xlink:type="locator" xlink:label="ufi_TheTermOfAFormerGroundLease" />
    <link:label xml:lang="en-US" xlink:label="ufi_TheTermOfAFormerGroundLease_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">The term of a former ground lease with E.I. DuPont de Nemours.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_TheTermOfAFormerGroundLease" xlink:to="ufi_TheTermOfAFormerGroundLease_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_TheTermOfAFormerGroundLease_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">The term of a former ground lease</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_TheTermOfAFormerGroundLease_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">The Term Of A Former Ground Lease</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NetMonitoringAndReportingCostsReveived_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net monitoring and reporting costs received</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NetMonitoringAndReportingCostsReveived_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Net Monitoring And Reporting Costs Reveived</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccountsReceivableRelatedParties" xlink:type="locator" xlink:label="us-gaap_AccountsReceivableRelatedParties" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableRelatedParties_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party receivables</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableRelatedParties" xlink:to="us-gaap_AccountsReceivableRelatedParties_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AccountsReceivableRelatedParties_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable Related Parties</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Related Party Transactions By Related Party [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Related Party Transactions By Related Party [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions By Related Party [Axis]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RelatedPartyDomain" xlink:type="locator" xlink:label="us-gaap_RelatedPartyDomain" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Related Party [Domain]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_SalemLeasingCorporationMember" xlink:type="locator" xlink:label="ufi_SalemLeasingCorporationMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_SalemLeasingCorporationMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Salem Leasing Corporation.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_SalemLeasingCorporationMember" xlink:to="ufi_SalemLeasingCorporationMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_SalemLeasingCorporationMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Salem Leasing Corporation</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_SalemLeasingCorporationMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Salem Leasing Corporation [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OperatingLeaseLiability" xlink:type="locator" xlink:label="us-gaap_OperatingLeaseLiability" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease obligations</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease Liability</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DueToRelatedPartiesCurrentAndNoncurrent" xlink:type="locator" xlink:label="us-gaap_DueToRelatedPartiesCurrentAndNoncurrent" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DueToRelatedPartiesCurrentAndNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total related party payables</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DueToRelatedPartiesCurrentAndNoncurrent" xlink:to="us-gaap_DueToRelatedPartiesCurrentAndNoncurrent_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_DueToRelatedPartiesCurrentAndNoncurrent_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Due To Related Parties Current And Noncurrent</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expenses with related party</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction Amounts Of Transaction</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="locator" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Segment Reporting Information By Segment [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Segment Reporting Information By Segment [Table]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_PolyesterMember" xlink:type="locator" xlink:label="ufi_PolyesterMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_PolyesterMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Refers to information regarding the polyester segment of the company.</link:label>
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    <link:label xml:lang="en-US" xlink:label="ufi_PolyesterMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Polyester [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_PolyesterMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Polyester [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_BrazilSegmentMember" xlink:type="locator" xlink:label="ufi_BrazilSegmentMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_BrazilSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Brazil segment.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_BrazilSegmentMember" xlink:to="ufi_BrazilSegmentMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_BrazilSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Brazil [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_BrazilSegmentMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Brazil Segment [Member]</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_NylonMember" xlink:type="locator" xlink:label="ufi_NylonMember" />
    <link:label xml:lang="en-US" xlink:label="ufi_NylonMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Nylon [member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_NylonMember" xlink:to="ufi_NylonMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_NylonMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Nylon [Member]</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_NylonMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Nylon [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AllOtherSegmentsMember" xlink:type="locator" xlink:label="us-gaap_AllOtherSegmentsMember" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">All Other [Member]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllOtherSegmentsMember" xlink:to="us-gaap_AllOtherSegmentsMember_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">All Other Segments [Member]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SegmentReportingInformationLineItems" xlink:type="locator" xlink:label="us-gaap_SegmentReportingInformationLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting Information [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingInformationLineItems" xlink:to="us-gaap_SegmentReportingInformationLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:type="locator" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciation" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment depreciation expense</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:to="us-gaap_CostOfGoodsAndServicesSoldDepreciation_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciation_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Goods And Services Sold Depreciation</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_SegmentProfitLoss_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Profit</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_SegmentProfitLoss_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Segment Profit Loss</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable" xlink:type="locator" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation Of Operating Profit Loss From Segments To Consolidated [Table]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable" xlink:to="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTable_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Reconciliation Of Operating Profit Loss From Segments To Consolidated [Table]</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems" xlink:type="locator" xlink:label="us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems" xlink:to="us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SegmentReportingReconcilingItemForOperatingProfitLossFromSegmentToConsolidatedLineItems_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_GrossProfit_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gross profit</link:label>
    <link:label xml:lang="en-US" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Selling, general and administrative expenses</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SupplementalCashFlowElementsAbstract" xlink:type="locator" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Elements [Abstract]</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowElementsAbstract" xlink:to="us-gaap_SupplementalCashFlowElementsAbstract_lbl" />
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InterestPaidNet" xlink:type="locator" xlink:label="us-gaap_InterestPaidNet" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest, net of capitalized interest of $221 and $92, respectively</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid Net</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeTaxesPaidNet" xlink:type="locator" xlink:label="us-gaap_IncomeTaxesPaidNet" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax payments, net</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxesPaidNet_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid Net</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InterestPaidCapitalized" xlink:type="locator" xlink:label="us-gaap_InterestPaidCapitalized" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestPaidCapitalized_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest capitalized</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidCapitalized" xlink:to="us-gaap_InterestPaidCapitalized_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_InterestPaidCapitalized_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid Capitalized</link:label>
    <link:loc xlink:href="ufi-20211226.xsd#ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes" xlink:type="locator" xlink:label="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes" />
    <link:label xml:lang="en-US" xlink:label="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation">Income tax payment related to recovery of non income taxes.</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes" xlink:to="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes_lbl" />
    <link:label xml:lang="en-US" xlink:label="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax payment related to recovery of non-income taxes</link:label>
    <link:label xml:lang="en-US" xlink:label="ufi_IncomeTaxPaymentRelatedToRecoveryOfNonIncomeTaxes_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Payment Related To Recovery Of Non Income Taxes</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="locator" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital expenditures incurred but not yet paid</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred But Not Yet Paid</link:label>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="locator" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" />
    <link:label xml:lang="en-US" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Non cash activity relating to finance leases</link:label>
    <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" />
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