Business Segment Information - Reconciliations of Segment Gross Profit to Consolidated Income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Dec. 27, 2020	Dec. 29, 2019	Dec. 27, 2020	Dec. 29, 2019
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 25,934	$ 15,665	$ 40,495	$ 33,108
Selling, general and administrative expenses	12,625	12,508	23,989	23,488
Benefit for bad debts	(259)	(258)	(1,146)	(249)
Other operating expense, net	476	854	1,654	962
Operating income	13,092	2,561	15,998	8,907
Interest income	(187)	(212)	(312)	(422)
Interest expense	833	1,101	1,704	2,358
Equity in (earnings) loss of unconsolidated affiliates	(130)	756	(223)	1,622
Income before income taxes	12,576	916	14,829	5,349
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	10,895	6,660	15,527	14,455
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	395	46	1,060	1,224
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	7,977	3,430	12,590	7,589
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	6,528	5,517	11,106	9,799
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 139	$ 12	$ 212	$ 41