Business Segment Information - Reconciliations of Segment Gross Profit (Loss) to Consolidated Income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended												12 Months Ended
	Jun. 24, 2018	[1]	Mar. 25, 2018	[1]	Dec. 24, 2017	[1]	Sep. 24, 2017	[1]	Jun. 25, 2017	Mar. 26, 2017	Dec. 25, 2016	Sep. 25, 2016	Jun. 24, 2018	Jun. 25, 2017	Jun. 26, 2016
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)	$ 23,904		$ 16,556		$ 22,676		$ 23,292		$ 27,357	$ 21,130	$ 22,130	$ 23,547	$ 86,428	$ 94,164	$ 93,632
SG&A expenses													56,077	50,829	47,502
(Benefit) provision for bad debts													(38)	(123)	1,684
Other operating expense (income), net													1,590	(310)	2,248
Operating income													28,799	43,768	42,198
Interest income													(560)	(517)	(610)
Interest expense													4,935	3,578	3,528
Loss on sale of business											$ 1,662			1,662
Equity in earnings of unconsolidated affiliates													(5,787)	(4,230)	(8,963)
Income before income taxes													30,211	43,275	48,243
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)													31,091	40,085	49,529
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)													10,484	12,071	17,809
International [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)													44,584	42,599	26,888
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)													$ 269	$ (591)	$ (594)

[1] Gross profit for the fiscal quarter ended March 25, 2018 includes the adverse impact of sustained raw material cost increases that could not be effectively offset with corresponding selling price increases.