Business Segment Information - Selected Financial Information for Polyester, Nylon, Brazil, Asia and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended																12 Months Ended
	Jun. 29, 2025		Mar. 30, 2025		Dec. 29, 2024		Sep. 29, 2024		Jun. 30, 2024		Mar. 31, 2024		Dec. 31, 2023		Oct. 01, 2023		Jun. 29, 2025	Jun. 30, 2024	Jul. 02, 2023
Segment Reporting Information [Line Items]
Net sales	$ 138,535	[1]	$ 146,557	[1]	$ 138,880	[1]	$ 147,372	[1]	$ 157,452	[2]	$ 148,996	[2]	$ 136,917	[2]	$ 138,844	[2]	$ 571,344	$ 582,209	$ 623,527
Cost of sales																	562,926	565,593	609,286
Gross (loss) profit	$ (1,129)	[3]	$ (445)	[3]	$ 534	[3]	$ 9,458	[3]	$ 10,791	[4]	$ 4,764	[4]	$ 1,636	[4]	$ (575)	[4]	8,418	16,616	14,241
Segment depreciation expense																	23,831	25,421	24,079
Segment Profit																	32,249	42,037	38,320
Americas [Member]
Segment Reporting Information [Line Items]
Net sales																	347,931	344,256	389,662
Cost of sales																	368,148	361,886	404,321
Gross (loss) profit																	(20,217)	(17,630)	(14,659)
Segment depreciation expense																	21,003	22,154	22,044
Segment Profit																	786	4,524	7,385
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales																	118,726	117,783	119,062
Cost of sales																	102,699	103,028	106,900
Gross (loss) profit																	16,027	14,755	12,162
Segment depreciation expense																	2,771	3,257	2,035
Segment Profit																	18,798	18,012	14,197
Asia [Member]
Segment Reporting Information [Line Items]
Net sales																	104,687	120,170	114,803
Cost of sales																	92,079	100,679	98,065
Gross (loss) profit																	12,608	19,491	16,738
Segment depreciation expense																	57	10
Segment Profit																	$ 12,665	$ 19,501	$ 16,738

[1] Net sales for fiscal 2025 includes lower volumes in the Americas and Asia Segments.

[2] Net sales for fiscal 2024 includes lower volumes in the Americas and Asia Segments as a result of lower global demand in connection with inventory destocking efforts of major brands and retailers.

[3] Gross profit (loss) for our domestic operations for all fiscal quarters of fiscal 2025 was impacted by softer sales and profitability in the Asia Segment and transition costs in the Americas Segment.

[4] Gross (loss) profit for our domestic operations for all fiscal quarters of fiscal 2024 was impacted by higher manufacturing costs and lower conversion margins.