Business Segment Information - Selected Financial Information for Polyester, Nylon, Brazil, Asia and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended																12 Months Ended
	Jun. 30, 2019		Mar. 31, 2019		Dec. 30, 2018		Sep. 30, 2018		Jun. 24, 2018		Mar. 25, 2018		Dec. 24, 2017		Sep. 24, 2017		Jun. 30, 2019	Jun. 24, 2018	Jun. 25, 2017
Segment Reporting Information [Line Items]
Net sales	$ 179,493	[1]	$ 179,989	[1]	$ 167,711	[1]	$ 181,611	[1]	$ 181,325		$ 165,867		$ 167,478		$ 164,242		$ 708,804	$ 678,912	$ 647,270
Cost of sales																	642,496	592,484	553,106
Gross profit	$ 18,342	[2]	$ 13,791	[2]	$ 14,156	[2]	$ 20,019	[2]	$ 23,904	[3]	$ 16,556	[3]	$ 22,676	[3]	$ 23,292	[3]	66,308	86,428	94,164
Segment depreciation expense																	19,917	19,994	17,803
Segment Profit																	86,225	106,422	111,967
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales																	370,770	364,169	355,740
Cost of sales																	346,951	330,975	315,655
Gross profit																	23,819	33,194	40,085
Segment depreciation expense																	16,068	15,893	13,921
Segment Profit																	39,887	49,087	54,006
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales																	98,127	102,639	112,704
Cost of sales																	90,231	92,155	100,633
Gross profit																	7,896	10,484	12,071
Segment depreciation expense																	2,083	2,197	2,125
Segment Profit																	9,979	12,681	14,196
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales																	102,877	110,587	109,079
Cost of sales																	84,298	84,726	82,463
Gross profit																	18,579	25,861	26,616
Segment depreciation expense																	1,537	1,648	1,119
Segment Profit																	20,116	27,509	27,735
Asia [Member]
Segment Reporting Information [Line Items]
Net sales																	132,866	97,297	64,607
Cost of sales																	117,166	80,677	48,624
Gross profit																	15,700	16,620	15,983
Segment Profit																	15,700	16,620	15,983
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales																	4,164	4,220	5,140
Cost of sales																	3,850	3,951	5,731
Gross profit																	314	269	(591)
Segment depreciation expense																	229	256	638
Segment Profit																	$ 543	$ 525	$ 47

[1] The fiscal quarter ended September 30, 2018 is comprised of fourteen weeks.

[2] 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.

[3] 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.