Business Segment Information - Reconciliations of Segment Gross Profit to Consolidated Income (loss) Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 28, 2021	Mar. 29, 2020	Mar. 28, 2021	Mar. 29, 2020
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 25,595	$ 15,383	$ 66,090	$ 48,491
Selling, general and administrative expenses	14,581	11,720	38,570	35,208
(Benefit) provision for bad debts	(184)	580	(1,330)	331
Other operating expense (income), net	2,582	(62)	4,236	900
Operating income	8,616	3,145	24,614	12,052
Interest income	(159)	(173)	(471)	(595)
Interest expense	885	1,231	2,589	3,589
Equity in earnings of unconsolidated affiliates	(528)	(3,526)	(751)	(1,904)
Impairment of investment in unconsolidated affiliate		45,194		45,194
Income (loss) before income taxes	8,418	(39,581)	23,247	(34,232)
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	7,222	7,032	22,749	21,487
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	437	333	1,497	1,557
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	10,598	3,416	23,188	11,005
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	7,153	4,583	18,259	14,382
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 185	$ 19	$ 397	$ 60