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. 30, 2019	[1]	Mar. 31, 2019	[1]	Dec. 30, 2018	[1]	Sep. 30, 2018	[1]	Jun. 24, 2018	[2]	Mar. 25, 2018	[2]	Dec. 24, 2017	[2]	Sep. 24, 2017	[2]	Jun. 30, 2019	Jun. 24, 2018	Jun. 25, 2017
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 18,342		$ 13,791		$ 14,156		$ 20,019		$ 23,904		$ 16,556		$ 22,676		$ 23,292		$ 66,308	$ 86,428	$ 94,164
SG&A expenses																	52,690	56,077	50,829
Provision (benefit) for bad debts																	308	(38)	(123)
Other operating expense (income), net																	2,350	1,590	(310)
Operating income																	10,960	28,799	43,768
Interest income																	(628)	(560)	(517)
Interest expense																	5,414	4,935	3,578
Loss on extinguishment of debt																	131
Loss on sale of business																			1,662
Equity in earnings of unconsolidated affiliates																	(3,968)	(5,787)	(4,230)
Income before income taxes																	10,011	30,211	43,275
Polyester [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	23,819	33,194	40,085
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	7,896	10,484	12,071
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	18,579	25,861	26,616
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	15,700	16,620	15,983
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	$ 314	$ 269	$ (591)

[1] Gross profit for the fiscal quarter ended December 30, 2018 includes the adverse impact of a raw material cost spike that could not be effectively offset with timely corresponding selling price increases. Gross profit for the fiscal quarters ended December 30, 2018, March 31, 2019 and June 30, 2019 includes the adverse impact of significant competitive pressure caused by elevated levels of polyester textured yarn imports.

[2] 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 timely corresponding selling price increases.