Business Segment Information - Selected Financial Information for Polyester, Nylon, Brazil, Asia and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended																12 Months Ended
	Jul. 03, 2022		Mar. 27, 2022		Dec. 26, 2021		Sep. 26, 2021		Jun. 27, 2021		Mar. 28, 2021		Dec. 27, 2020		Sep. 27, 2020		Jul. 03, 2022	Jun. 27, 2021	Jun. 28, 2020
Segment Reporting Information [Line Items]
Net sales	$ 217,576	[1]	$ 200,780	[1]	$ 201,410	[1]	$ 195,992	[1]	$ 184,445	[2]	$ 178,866	[2]	$ 162,776	[2]	$ 141,505	[2]	$ 815,758	$ 667,592	$ 606,509
Cost of sales																	735,273	574,098	567,469
Gross profit	$ 18,354	[3]	$ 19,144	[3]	$ 16,890	[3]	$ 26,097	[3]	$ 27,404	[4]	$ 25,595	[4]	$ 25,934	[4]	$ 14,561	[4]	80,485	93,494	39,040
Segment depreciation expense																	22,653	22,369	20,659
Segment Profit																	103,138	115,863	59,699
Americas [Member]
Segment Reporting Information [Line Items]
Net sales																	483,085	386,779	380,138
Cost of sales																	458,617	350,373	368,976
Gross profit																	24,468	36,406	11,162
Segment depreciation expense																	21,153	21,054	19,274
Segment Profit																	45,621	57,460	30,436
Brazil [Member]
Segment Reporting Information [Line Items]
Net sales																	126,066	95,976	73,339
Cost of sales																	98,925	64,281	62,144
Gross profit																	27,141	31,695	11,195
Segment depreciation expense																	1,500	1,315	1,385
Segment Profit																	28,641	33,010	12,580
Asia [Member]
Segment Reporting Information [Line Items]
Net sales																	206,607	184,837	153,032
Cost of sales																	177,731	159,444	136,349
Gross profit																	28,876	25,393	16,683
Segment Profit																	$ 28,876	$ 25,393	$ 16,683

[1] The fiscal quarter ending July 3, 2022 included an additional week of sales of approximately $8,700.

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

[3] Gross profit for our domestic operations for all fiscal quarters of fiscal 2022 includes adverse pressures from (i) higher raw material costs, (ii) rising input costs, and (iii) the weakening of labor productivity.

[4] 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.