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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
Jun. 30, 2024
Mar. 31, 2024
Dec. 31, 2023
Oct. 01, 2023
Jul. 02, 2023
Apr. 02, 2023
Jan. 01, 2023
Oct. 02, 2022
Jun. 30, 2024
Jul. 02, 2023
Jul. 03, 2022
Segment Reporting Information [Line Items]                      
Net sales $ 157,452 [1] $ 148,996 [1] $ 136,917 [1] $ 138,844 [1] $ 151,058 [2] $ 156,738 [2] $ 136,212 [2] $ 179,519 [2] $ 582,209 $ 623,527 $ 815,758
Cost of sales                 565,593 609,286 735,273
Gross (loss) profit $ 10,791 [3] $ 4,764 [3] $ 1,636 [3] $ (575) [3] $ 6,025 [4] $ 9,653 [4] $ (8,000) [4] $ 6,563 [4] 16,616 14,241 80,485
Segment depreciation expense                 25,421 24,079 22,653
Segment Profit                 42,037 38,320 103,138
Americas [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 344,256 389,662 483,085
Cost of sales                 361,886 404,321 458,617
Gross (loss) profit                 (17,630) (14,659) 24,468
Segment depreciation expense                 22,154 22,044 21,153
Segment Profit                 4,524 7,385 45,621
Brazil [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 117,783 119,062 126,066
Cost of sales                 103,028 106,900 98,925
Gross (loss) profit                 14,755 12,162 27,141
Segment depreciation expense                 3,257 2,035 1,500
Segment Profit                 18,012 14,197 28,641
Asia [Member]                      
Segment Reporting Information [Line Items]                      
Net sales                 120,170 114,803 206,607
Cost of sales                 100,679 98,065 177,731
Gross (loss) profit                 19,491 16,738 28,876
Segment depreciation expense                 10    
Segment Profit                 $ 19,501 $ 16,738 $ 28,876
[1] Net sales for fiscal 2024 includes lower volumes in the Americas and Asia Segments as a result of lower global demand in connection with inventory destocking efforts of major brands and retailers.
[2] Net sales for all fiscal quarters of fiscal 2023 includes adverse demand pressures in the Americas and Asia Segments.
[3] Gross (loss) profit for our domestic operations for all fiscal quarters of fiscal 2024 was impacted by higher manufacturing costs and lower conversion margins.
[4] Gross profit (loss) 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.