Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 28, 2021	Mar. 29, 2020	Mar. 28, 2021	Mar. 29, 2020
Segment Reporting Information [Line Items]
Net sales	$ 178,866	$ 170,994	$ 483,147	$ 520,454
Cost of sales	153,271	155,611	417,057	471,963
Gross profit	25,595	15,383	66,090	48,491
Segment depreciation expense	5,937	5,330	16,769	15,443
Segment Profit	31,532	20,713	82,859	63,934
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	82,668	89,767	228,440	261,212
Cost of sales	75,446	82,735	205,691	239,725
Gross profit	7,222	7,032	22,749	21,487
Segment depreciation expense	5,036	4,301	13,909	12,525
Segment Profit	12,258	11,333	36,658	34,012
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	48,483	38,621	130,898	132,496
Cost of sales	41,330	34,038	112,639	118,114
Gross profit	7,153	4,583	18,259	14,382
Segment Profit	7,153	4,583	18,259	14,382
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	25,704	21,060	72,563	66,094
Cost of sales	15,106	17,644	49,375	55,089
Gross profit	10,598	3,416	23,188	11,005
Segment depreciation expense	299	421	1,050	1,153
Segment Profit	10,897	3,837	24,238	12,158
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	20,778	20,567	47,815	57,853
Cost of sales	20,341	20,234	46,318	56,296
Gross profit	437	333	1,497	1,557
Segment depreciation expense	441	471	1,321	1,465
Segment Profit	878	804	2,818	3,022
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales	1,233	979	3,431	2,799
Cost of sales	1,048	960	3,034	2,739
Gross profit	185	19	397	60
Segment depreciation expense	161	137	489	300
Segment Profit	$ 346	$ 156	$ 886	$ 360