Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jan. 01, 2023	Dec. 26, 2021	Jan. 01, 2023	Dec. 26, 2021
Segment Reporting Information [Line Items]
Net sales	$ 136,212	$ 201,410	$ 315,731	$ 397,402
Cost of sales	144,212	184,520	317,168	354,415
Gross (loss) profit	(8,000)	16,890	(1,437)	42,987
Segment depreciation expense	5,933	5,422	11,883	10,880
Segment (Loss) Profit	(2,067)	22,312	10,446	53,867
Americas [Member]
Segment Reporting Information [Line Items]
Net sales	85,242	114,697	192,886	225,523
Cost of sales	98,326	113,844	210,839	215,484
Gross (loss) profit	(13,084)	853	(17,953)	10,039
Segment depreciation expense	5,542	5,145	11,022	10,220
Segment (Loss) Profit	(7,542)	5,998	(6,931)	20,259
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	25,687	27,601	64,566	61,339
Cost of sales	24,357	20,075	56,449	43,873
Gross (loss) profit	1,330	7,526	8,117	17,466
Segment depreciation expense	391	277	861	660
Segment (Loss) Profit	1,721	7,803	8,978	18,126
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	25,283	59,112	58,279	110,540
Cost of sales	21,529	50,601	49,880	95,058
Gross (loss) profit	3,754	8,511	8,399	15,482
Segment (Loss) Profit	$ 3,754	$ 8,511	$ 8,399	$ 15,482