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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. 02, 2023
Apr. 02, 2023
Jan. 01, 2023
Oct. 02, 2022
Jul. 03, 2022
Mar. 27, 2022
Dec. 26, 2021
Sep. 26, 2021
Jul. 02, 2023
Jul. 03, 2022
Jun. 27, 2021
Segment Reporting Information [Line Items]                      
Net sales $ 151,058 [1] $ 156,738 [1] $ 136,212 [1] $ 179,519 [1] $ 217,576 [2] $ 200,780 [2] $ 201,410 [2] $ 195,992 [2] $ 623,527 $ 815,758 $ 667,592
Cost of sales                 609,286 735,273 574,098
Gross (loss) profit $ 6,025 [3] $ 9,653 [3] $ (8,000) [3] $ 6,563 [3] $ 18,354 [4] $ 19,144 [4] $ 16,890 [4] $ 26,097 [4] 14,241 80,485 93,494
Segment depreciation expense                 24,079 22,653 22,369
Segment Profit                 38,320 103,138 115,863
Americas [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 389,662 483,085 386,779
Cost of sales                 404,321 458,617 350,373
Gross (loss) profit                 (14,659) 24,468 36,406
Segment depreciation expense                 22,044 21,153 21,054
Segment Profit                 7,385 45,621 57,460
Brazil [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 119,062 126,066 95,976
Cost of sales                 106,900 98,925 64,281
Gross (loss) profit                 12,162 27,141 31,695
Segment depreciation expense                 2,035 1,500 1,315
Segment Profit                 14,197 28,641 33,010
Asia [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 114,803 206,607 184,837
Cost of sales                 98,065 177,731 159,444
Gross (loss) profit                 16,738 28,876 25,393
Segment Profit                 $ 16,738 $ 28,876 $ 25,393
[1] Net sales for all fiscal quarters of fiscal 2023 includes adverse demand pressures in the Americas and Asia Segments.
[2] The fiscal quarter ending July 3, 2022 included an additional week of sales of approximately $8,700.
[3] Gross profit for our domestic operations for all fiscal quarters of fiscal 2023 was impacted by lower production volumes driving weaker fixed cost absorption in connection with lower sales volumes.
[4] 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.