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. 29, 2020	Mar. 31, 2019	Mar. 29, 2020	Mar. 31, 2019
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 15,383	$ 13,791	$ 48,491	$ 47,966
Selling, general and administrative expenses	11,720	11,439	35,208	40,672
Provision for bad debts	580	218	331	381
Other operating (income) expense, net	(62)	1,359	900	1,218
Operating income	3,145	775	12,052	5,695
Interest income	(173)	(149)	(595)	(448)
Interest expense	1,231	1,256	3,589	4,078
Equity in earnings of unconsolidated affiliates	(3,526)	(1,873)	(1,904)	(3,126)
Impairment of investment in unconsolidated affiliate	45,194		45,194
Loss on extinguishment of debt				131
(Loss) income before income taxes	(39,581)	1,541	(34,232)	5,060
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	7,032	4,804	21,487	15,917
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	333	2,312	1,557	6,488
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	3,416	2,776	11,005	13,603
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	4,583	3,841	14,382	11,697
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 19	$ 58	$ 60	$ 261