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. 28, 2020		Mar. 29, 2020		Dec. 29, 2019		Sep. 29, 2019		Jun. 30, 2019		Mar. 31, 2019		Dec. 30, 2018		Sep. 30, 2018		Jun. 28, 2020	Jun. 28, 2020	Jun. 30, 2019	Jun. 24, 2018	Jun. 24, 2018
Segment Reporting Information [Line Items]
Net sales	$ 86,055	[1]	$ 170,994	[1]	$ 169,511	[1]	$ 179,949	[1]	$ 179,493	[2]	$ 179,989	[2]	$ 167,711	[2]	$ 181,611	[2]	$ 606,509	$ 606,509	$ 708,804	$ 678,912
Cost of sales																	567,469	567,469	642,496	592,484
Gross profit	$ (9,451)	[3]	$ 15,383	[3]	$ 15,665	[3]	$ 17,443	[3]	$ 18,342	[4]	$ 13,791	[4]	$ 14,156	[4]	$ 20,019	[4]	39,040	39,040	66,308	86,428
Segment depreciation expense																	20,659		19,917	19,994
Segment Profit																	59,699		86,225	106,422
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales																	309,184		370,770	364,169
Cost of sales																	297,096		346,951	330,975
Gross profit																	12,088	12,088	23,819	33,194
Segment depreciation expense																	16,904		16,068	15,893
Segment Profit																	28,992		39,887	49,087
Asia [Member]
Segment Reporting Information [Line Items]
Net sales																	153,032		132,866		$ 97,297
Cost of sales																	136,349		117,166		80,677
Gross profit																	16,683	16,683	15,700	16,620	16,620
Segment Profit																	16,683		15,700		$ 16,620
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales																	73,339		102,877	110,587
Cost of sales																	62,144		84,298	84,726
Gross profit																	11,195	11,195	18,579	25,861
Segment depreciation expense																	1,385		1,537	1,648
Segment Profit																	12,580		20,116	27,509
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales																	67,381		98,127	102,639
Cost of sales																	68,359		90,231	92,155
Gross profit																	(978)	(978)	7,896	10,484
Segment depreciation expense																	1,917		2,083	2,197
Segment Profit																	939		9,979	12,681
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales																	3,573		4,164	4,220
Cost of sales																	3,521		3,850	3,951
Gross profit																	52	$ 52	314	269
Segment depreciation expense																	453		229	256
Segment Profit																	$ 505		$ 543	$ 525

[1] Net sales for the fiscal quarter ended June 28, 2020, includes the impact of global demand declines and decreased economic activity caused by the COVID-19 pandemic

[2] The fiscal quarter ended September 30, 2018 was comprised of fourteen weeks.

[3] Gross loss for the fiscal quarter ended June 28, 2020 includes the adverse impact of lower fixed cost absorption in connection with the COVID-19 pandemic.

[4] 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 and March 31, 2019 includes the adverse impact of significant competitive pressure caused by elevated levels of polyester textured yarn imports.