Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023
Segment Reporting Information [Line Items]
Net sales	$ 148,996	$ 156,738	$ 424,757	$ 472,469
Cost of sales	144,232	147,085	418,932	464,253
Gross profit	4,764	9,653	5,825	8,216
Segment depreciation expense	6,314	6,123	18,925	18,006
Segment (Loss) Profit	11,078	15,776	24,750	26,222
Americas [Member]
Segment Reporting Information [Line Items]
Net sales	91,130	101,946	253,252	294,832
Cost of sales	94,644	98,788	270,884	309,627
Gross profit	(3,514)	3,158	(17,632)	(14,795)
Segment depreciation expense	5,473	5,574	16,478	16,596
Segment (Loss) Profit	1,959	8,732	(1,154)	1,801
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	29,573	27,380	85,543	91,946
Cost of sales	25,736	24,998	76,400	81,447
Gross profit	3,837	2,382	9,143	10,499
Segment depreciation expense	841	549	2,447	1,410
Segment (Loss) Profit	4,678	2,931	11,590	11,909
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	28,293	27,412	85,962	85,691
Cost of sales	23,852	23,299	71,648	73,179
Gross profit	4,441	4,113	14,314	12,512
Segment (Loss) Profit	$ 4,441	$ 4,113	$ 14,314	$ 12,512