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Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Dec. 29, 2024
Dec. 31, 2023
Dec. 29, 2024
Dec. 31, 2023
Segment Reporting Information [Line Items]        
Net sales $ 138,880 $ 136,917 $ 286,252 $ 275,761
Cost of sales 138,346 135,281 276,260 274,700
Gross profit 534 1,636 9,992 1,061
Segment depreciation expense 5,950 6,274 12,118 12,611
Segment (Loss) Profit 6,484 7,910 22,110 13,672
Americas [Member]        
Segment Reporting Information [Line Items]        
Net sales 83,095 80,549 169,378 162,122
Cost of sales 89,635 87,287 177,296 176,240
Gross profit (6,540) (6,738) (7,918) (14,118)
Segment depreciation expense 5,334 5,508 10,744 11,005
Segment (Loss) Profit (1,206) (1,230) 2,826 (3,113)
Brazil [Member]        
Segment Reporting Information [Line Items]        
Net sales 27,482 26,061 61,792 55,970
Cost of sales 23,696 22,922 50,069 50,664
Gross profit 3,786 3,139 11,723 5,306
Segment depreciation expense 602 766 1,343 1,606
Segment (Loss) Profit 4,388 3,905 13,066 6,912
Asia [Member]        
Segment Reporting Information [Line Items]        
Net sales 28,303 30,307 55,082 57,669
Cost of sales 25,015 25,072 48,895 47,796
Gross profit 3,288 5,235 6,187 9,873
Segment depreciation expense 14   31  
Segment (Loss) Profit $ 3,302 $ 5,235 $ 6,218 $ 9,873