Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended
	Sep. 26, 2021	Sep. 27, 2020
Segment Reporting Information [Line Items]
Net sales	$ 195,992	$ 141,505
Cost of sales	169,895	126,944
Gross profit	26,097	14,561
Segment depreciation expense	5,458	5,439
Segment Profit	31,555	20,000
Polyester
Segment Reporting Information [Line Items]
Net sales	89,467	69,076
Cost of sales	81,173	64,444
Gross profit	8,294	4,632
Segment depreciation expense	4,482	4,403
Segment Profit	12,776	9,035
Asia [Member]
Segment Reporting Information [Line Items]
Net sales	51,428	37,723
Cost of sales	44,457	33,145
Gross profit	6,971	4,578
Segment Profit	6,971	4,578
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales	33,738	22,606
Cost of sales	23,798	17,993
Gross profit	9,940	4,613
Segment depreciation expense	383	430
Segment Profit	10,323	5,043
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	20,159	11,029
Cost of sales	19,433	10,364
Gross profit	726	665
Segment depreciation expense	435	442
Segment Profit	1,161	1,107
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales	1,200	1,071
Cost of sales	1,034	998
Gross profit	166	73
Segment depreciation expense	158	164
Segment Profit	$ 324	$ 237