Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Apr. 02, 2023	Mar. 27, 2022	Apr. 02, 2023	Mar. 27, 2022
Segment Reporting Information [Line Items]
Net sales	$ 156,738	$ 200,780	$ 472,469	$ 598,182
Cost of sales	147,085	181,636	464,253	536,051
Gross profit	9,653	19,144	8,216	62,131
Segment depreciation expense	6,123	5,608	18,006	16,488
Segment Profit	15,776	24,752	26,222	78,619
Americas [Member]
Segment Reporting Information [Line Items]
Net sales	101,946	119,736	294,832	345,259
Cost of sales	98,788	113,952	309,627	329,436
Gross profit	3,158	5,784	(14,795)	15,823
Segment depreciation expense	5,574	5,226	16,596	15,446
Segment Profit	8,732	11,010	1,801	31,269
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	27,380	29,767	91,946	91,106
Cost of sales	24,998	23,784	81,447	67,657
Gross profit	2,382	5,983	10,499	23,449
Segment depreciation expense	549	382	1,410	1,042
Segment Profit	2,931	6,365	11,909	24,491
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	27,412	51,277	85,691	161,817
Cost of sales	23,299	43,900	73,179	138,958
Gross profit	4,113	7,377	12,512	22,859
Segment Profit	$ 4,113	$ 7,377	$ 12,512	$ 22,859