Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Dec. 31, 2023	Jan. 01, 2023
Segment Reporting Information [Line Items]
Net sales	$ 136,917	$ 136,212	$ 275,761	$ 315,731
Cost of sales	135,281	144,212	274,700	317,168
Gross profit (loss)	1,636	(8,000)	1,061	(1,437)
Segment depreciation expense	6,274	5,933	12,611	11,883
Segment (Loss) Profit	7,910	(2,067)	13,672	10,446
Americas [Member]
Segment Reporting Information [Line Items]
Net sales	80,549	85,242	162,122	192,886
Cost of sales	87,287	98,326	176,240	210,839
Gross profit (loss)	(6,738)	(13,084)	(14,118)	(17,953)
Segment depreciation expense	5,508	5,542	11,005	11,022
Segment (Loss) Profit	(1,230)	(7,542)	(3,113)	(6,931)
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	26,061	25,687	55,970	64,566
Cost of sales	22,922	24,357	50,664	56,449
Gross profit (loss)	3,139	1,330	5,306	8,117
Segment depreciation expense	766	391	1,606	861
Segment (Loss) Profit	3,905	1,721	6,912	8,978
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	30,307	25,283	57,669	58,279
Cost of sales	25,072	21,529	47,796	49,880
Gross profit (loss)	5,235	3,754	9,873	8,399
Segment (Loss) Profit	$ 5,235	$ 3,754	$ 9,873	$ 8,399