Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 27, 2022	Mar. 28, 2021	Mar. 27, 2022	Mar. 28, 2021
Segment Reporting Information [Line Items]
Net sales	$ 200,780	$ 178,866	$ 598,182	$ 483,147
Cost of sales	181,636	153,271	536,051	417,057
Gross profit	19,144	25,595	62,131	66,090
Segment depreciation expense	5,608	5,937	16,488	16,769
Segment Profit	24,752	31,532	78,619	82,859
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	93,924	82,668	275,809	228,440
Cost of sales	90,043	75,446	263,194	205,691
Gross profit	3,881	7,222	12,615	22,749
Segment depreciation expense	4,642	5,036	13,668	13,909
Segment Profit	8,523	12,258	26,283	36,658
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	51,277	48,483	161,817	130,898
Cost of sales	43,900	41,330	138,958	112,639
Gross profit	7,377	7,153	22,859	18,259
Segment Profit	7,377	7,153	22,859	18,259
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	29,767	25,704	91,106	72,563
Cost of sales	23,784	15,106	67,657	49,375
Gross profit	5,983	10,598	23,449	23,188
Segment depreciation expense	382	299	1,042	1,050
Segment Profit	6,365	10,897	24,491	24,238
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	24,689	20,778	65,863	47,815
Cost of sales	22,925	20,341	63,187	46,318
Gross profit	1,764	437	2,676	1,497
Segment depreciation expense	441	441	1,320	1,321
Segment Profit	2,205	878	3,996	2,818
All Other [Member]
Segment Reporting Information [Line Items]
Net sales	1,123	1,233	3,587	3,431
Cost of sales	984	1,048	3,055	3,034
Gross profit	139	185	532	397
Segment depreciation expense	143	161	458	489
Segment Profit	$ 282	$ 346	$ 990	$ 886