Business Segment Information - Reconciliations of Segment Gross Profit to Consolidated Income (loss) Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended																12 Months Ended
	Jun. 27, 2021	[1]	Mar. 28, 2021	[1]	Dec. 27, 2020	[1]	Sep. 27, 2020	[1]	Jun. 28, 2020	[2]	Mar. 29, 2020	[2]	Dec. 29, 2019	[2]	Sep. 29, 2019	[2]	Jun. 27, 2021	Jun. 28, 2020	Jun. 30, 2019	Jun. 30, 2019
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 27,404		$ 25,595		$ 25,934		$ 14,561		$ (9,451)		$ 15,383		$ 15,665		$ 17,443		$ 93,494	$ 39,040	$ 66,308
Selling, general and administrative expenses																	51,334	43,814	52,690
(Benefit) provision for bad debts																	(1,316)	1,739	308
Other operating expense, net																	4,865	2,308	2,350
Operating income (loss)																	38,611	(8,821)	10,960
Interest income																	(603)	(722)	(628)
Interest expense																	3,323	4,779	5,414
Equity in (earnings) loss of unconsolidated affiliates																	(739)	477	(3,968)
Recovery of non-income taxes																	(9,717)
Gain on sale of investment in unconsolidated affiliate																		(2,284)
Impairment of investment in unconsolidated affiliate																		45,194
Loss on extinguishment of debt																			131
Income (loss) before income taxes																	46,347	(56,265)	10,011
Polyester
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	33,444	12,088	23,819
Nylon [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	2,367	(978)	7,896
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	31,695	11,195	18,579
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	25,393	16,683	15,700	$ 15,700
Other Segments [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	$ 595	$ 52	$ 314

[1] 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.

[2] 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.