Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 31, 2019	Mar. 25, 2018	Mar. 31, 2019	Mar. 25, 2018
Segment Reporting Information [Line Items]
Net sales	$ 179,989	$ 165,867	$ 529,311	$ 497,587
Cost of sales	166,198	149,311	481,345	435,063
Gross profit	13,791	16,556	47,966	62,524
Segment depreciation expense	4,841	5,084	14,959	14,955
Segment Profit	18,632	21,640	62,925	77,479
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	95,745	88,763	281,665	266,817
Cost of sales	92,221	83,948	269,444	244,513
Gross profit	3,524	4,815	12,221	22,304
Segment depreciation expense	3,858	4,022	12,047	11,862
Segment Profit	7,382	8,837	24,268	34,166
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	25,563	24,036	76,159	75,966
Cost of sales	23,251	23,023	69,671	68,563
Gross profit	2,312	1,013	6,488	7,403
Segment depreciation expense	516	560	1,576	1,649
Segment Profit	2,828	1,573	8,064	9,052
International [Member]
Segment Reporting Information [Line Items]
Net sales	57,681	51,989	168,271	151,694
Cost of sales	49,784	41,317	139,275	119,050
Gross profit	7,897	10,672	28,996	32,644
Segment depreciation expense	420	436	1,146	1,249
Segment Profit	8,317	11,108	30,142	33,893
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales	1,000	1,079	3,216	3,110
Cost of sales	942	1,023	2,955	2,937
Gross profit	58	56	261	173
Segment depreciation expense	47	66	190	195
Segment Profit	$ 105	$ 122	$ 451	$ 368