Derivative Financial Instruments - Derivatives Subject to a Master Netting Arrangement (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Liabilities
Gross amounts not offset in the statement of financial position, cash collateral	$ 114	$ 63
Derivatives designated as hedging instruments
Liabilities
Gross Amount	1
Gross Amounts Netted in the Statements of Financial Position	0
Net Amount Presented in the Statements of Financial Position	1
Gross amounts not offset in the statement of financial position, financial instrument	0
Gross amounts not offset in the statement of financial position, cash collateral	14	29
Derivatives designated as hedging instruments \| Interest rate swaps on AFS securities
Liabilities
Gross Amount	0
Gross Amounts Netted in the Statements of Financial Position	0
Net Amount Presented in the Statements of Financial Position	0
Gross amounts not offset in the statement of financial position, financial instrument	0
Gross amounts not offset in the statement of financial position, cash collateral	5
Derivatives designated as hedging instruments \| Interest rate swaps on HFI residential first mortgages
Liabilities
Gross Amount	0
Gross Amounts Netted in the Statements of Financial Position	0
Net Amount Presented in the Statements of Financial Position	0
Gross amounts not offset in the statement of financial position, financial instrument	0
Gross amounts not offset in the statement of financial position, cash collateral	1
Derivatives designated as hedging instruments \| Interest rate swaps on custodial deposits
Liabilities
Gross Amount	1
Gross Amounts Netted in the Statements of Financial Position	0
Net Amount Presented in the Statements of Financial Position	1
Gross amounts not offset in the statement of financial position, financial instrument	0
Gross amounts not offset in the statement of financial position, cash collateral	8
Derivatives not designated as hedging instruments
Liabilities
Gross Amount	102	17
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	102	17
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	94	63
Asset
Gross Amount	73	28
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	73	28
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	6	0
Derivatives not designated as hedging instruments \| Mortgage-backed securities forwards
Liabilities
Gross Amount	98	9
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	98	9
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	68	24
Asset
Gross Amount	14	2
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	14	2
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	0	0
Derivatives not designated as hedging instruments \| Interest rate swaps
Asset
Gross Amount	59	26
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	59	26
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	6	0
Derivatives not designated as hedging instruments \| Interest rate swaps and swaptions
Liabilities
Gross Amount	4	8
Gross Amounts Netted in the Statements of Financial Position	0	0
Net Amount Presented in the Statements of Financial Position	4	8
Gross amounts not offset in the statement of financial position, financial instrument	0	0
Gross amounts not offset in the statement of financial position, cash collateral	$ 26	$ 39

Fair value of liability associated with financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4B
-Subparagraph (a),(c)
-URI http://asc.fasb.org/extlink&oid=121590274&loc=SL5624163-113959

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226003-175313

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

+ Details

Name:	us-gaap_DerivativeAssetFairValueGrossLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value, after the effects of master netting arrangements, of a financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes assets not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121572278&loc=d3e13433-108611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

+ Details

Name:	us-gaap_DerivativeAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_DerivativeAssetsAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of obligation to return cash collateral under master netting arrangements that have not been offset against derivative assets.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226016-175313

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121590274&loc=d3e41678-113959

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (d)(2)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

+ Details

Name:	us-gaap_DerivativeCollateralObligationToReturnCash
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of obligation to return securities collateral under master netting arrangements that have not been offset against derivative assets.

+ References

+ Details

Name:	us-gaap_DerivativeCollateralObligationToReturnSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of right to receive cash collateral under master netting arrangements that have not been offset against derivative liabilities.

+ References

+ Details

Name:	us-gaap_DerivativeCollateralRightToReclaimCash
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of right to receive securities collateral under master netting arrangements that have not been offset against derivative liabilities.

+ References

+ Details

Name:	us-gaap_DerivativeCollateralRightToReclaimSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Fair value, before effects of master netting arrangements, of a financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes assets elected not to be offset. Excludes assets not subject to a master netting arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226000-175313

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 860
-SubTopic 20
-Section 50
-Paragraph 4D
-Subparagraph (c)(2)
-URI http://asc.fasb.org/extlink&oid=121570589&loc=SL51823488-111719

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4B
-Subparagraph (a),(c)
-URI http://asc.fasb.org/extlink&oid=121590274&loc=SL5624163-113959

+ Details

Name:	us-gaap_DerivativeFairValueOfDerivativeAsset
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Fair value, before effects of master netting arrangements, of a financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes liabilities elected not to be offset. Excludes liabilities not subject to a master netting arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 860
-SubTopic 20
-Section 50
-Paragraph 4D
-Subparagraph (c)(2)
-URI http://asc.fasb.org/extlink&oid=121570589&loc=SL51823488-111719

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4B
-Subparagraph (a),(c)
-URI http://asc.fasb.org/extlink&oid=121590274&loc=SL5624163-113959

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226000-175313

+ Details

Name:	us-gaap_DerivativeFairValueOfDerivativeLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value, after the effects of master netting arrangements, of a financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes liabilities not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121572278&loc=d3e13433-108611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

+ Details

Name:	us-gaap_DerivativeLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_DerivativeLiabilitiesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Fair value of asset associated with financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226003-175313

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4B
-Subparagraph (a),(c)
-URI http://asc.fasb.org/extlink&oid=121590274&loc=SL5624163-113959

+ Details

Name:	us-gaap_DerivativeLiabilityFairValueGrossAsset
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=fbc_InterestRateSwapsAvailableForSaleSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=fbc_InterestRateSwapsOnHFIResidentialFirstMortgagesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=fbc_InterestRateSwapsFHLBAdvancesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_NondesignatedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_MortgageBackedSecuritiesOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=fbc_InterestRateSwapsandSwaptionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: