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. 27, 2021		Mar. 28, 2021		Dec. 27, 2020		Sep. 27, 2020		Jun. 28, 2020		Mar. 29, 2020		Dec. 29, 2019		Sep. 29, 2019		Jun. 27, 2021	Jun. 28, 2020	Jun. 30, 2019	Jun. 30, 2019
Segment Reporting Information [Line Items]
Net sales	$ 184,445	[1]	$ 178,866	[1]	$ 162,776	[1]	$ 141,505	[1]	$ 86,055	[2]	$ 170,994	[2]	$ 169,511	[2]	$ 179,949	[2]	$ 667,592	$ 606,509	$ 708,804
Cost of sales																	574,098	567,469	642,496
Gross profit	$ 27,404	[3]	$ 25,595	[3]	$ 25,934	[3]	$ 14,561	[3]	$ (9,451)	[4]	$ 15,383	[4]	$ 15,665	[4]	$ 17,443	[4]	93,494	39,040	66,308
Segment depreciation expense																	22,369	20,659	19,917
Segment Profit																	115,863	59,699	86,225
Polyester
Segment Reporting Information [Line Items]
Net sales																	316,235	309,184	370,770
Cost of sales																	282,791	297,096	346,951
Gross profit																	33,444	12,088	23,819
Segment depreciation expense																	18,637	16,904	16,068
Segment Profit																	52,081	28,992	39,887
Asia [Member]
Segment Reporting Information [Line Items]
Net sales																	184,837	153,032		$ 132,866
Cost of sales																	159,444	136,349		117,166
Gross profit																	25,393	16,683	15,700	15,700
Segment Profit																	25,393	16,683		$ 15,700
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales																	95,976	73,339	102,877
Cost of sales																	64,281	62,144	84,298
Gross profit																	31,695	11,195	18,579
Segment depreciation expense																	1,315	1,385	1,537
Segment Profit																	33,010	12,580	20,116
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales																	65,869	67,381	98,127
Cost of sales																	63,502	68,359	90,231
Gross profit																	2,367	(978)	7,896
Segment depreciation expense																	1,769	1,917	2,083
Segment Profit																	4,136	939	9,979
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales																	4,675	3,573	4,164
Cost of sales																	4,080	3,521	3,850
Gross profit																	595	52	314
Segment depreciation expense																	648	453	229
Segment Profit																	$ 1,243	$ 505	$ 543

[1] Net sales for the fiscal quarters ended September 27, 2020 and December 27, 2020 includes adverse demand pressures from the COVID-19 pandemic

[2] 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.

[3] Gross profit for the fiscal quarter ended September 27, 2020 includes adverse demand pressures from the COVID-19 pandemic. Gross profit for the fiscal quarters ended December 27, 2020, March 28, 2021 and June 27, 2021 includes the benefit of exceptional performance by the Brazil Segment primarily due to higher conversion margin and market share capture due to agility and responsiveness during demand recovery in Brazil.

[4] 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.