Business Segment Information - Reconciliations of Segment Gross Profit to Consolidated Income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 27, 2022	Mar. 28, 2021	Mar. 27, 2022	Mar. 28, 2021
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 19,144	$ 25,595	$ 62,131	$ 66,090
Selling, general and administrative expenses	14,389	14,581	39,025	38,570
Benefit for bad debts	(169)	(184)	(489)	(1,330)
Other operating (income) expense, net	(831)	2,582	(2)	4,236
Operating income	5,755	8,616	23,597	24,614
Interest income	(492)	(159)	(944)	(471)
Interest expense	709	885	2,140	2,589
Equity in earnings of unconsolidated affiliates	(41)	(528)	(385)	(751)
Recovery of non-income taxes, net	815		815
Income before income taxes	4,764	8,418	21,971	23,247
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	3,881	7,222	12,615	22,749
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	1,764	437	2,676	1,497
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	5,983	10,598	23,449	23,188
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	7,377	7,153	22,859	18,259
All Other [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 139	$ 185	$ 532	$ 397