Business Segment Information - Selected Financial Information for Polyester, Nylon, International and Other Segments (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 25, 2018	Mar. 26, 2017	Mar. 25, 2018	Mar. 26, 2017
Segment Reporting Information [Line Items]
Net sales	$ 165,867	$ 160,896	$ 497,587	$ 476,020
Cost of sales	149,311	139,766	435,063	409,213
Gross profit	16,556	21,130	62,524	66,807
Segment depreciation expense	5,084	4,569	14,955	13,071
Segment Profit (Loss)	21,640	25,699	77,479	79,878
Polyester [Member]
Segment Reporting Information [Line Items]
Net sales	88,763	90,267	266,817	261,623
Cost of sales	83,948	81,730	244,513	234,165
Gross profit	4,815	8,537	22,304	27,458
Segment depreciation expense	4,022	3,636	11,862	10,128
Segment Profit (Loss)	8,837	12,173	34,166	37,586
Nylon [Member]
Segment Reporting Information [Line Items]
Net sales	24,036	26,987	75,966	83,784
Cost of sales	23,023	24,656	68,563	75,693
Gross profit	1,013	2,331	7,403	8,091
Segment depreciation expense	560	542	1,649	1,582
Segment Profit (Loss)	1,573	2,873	9,052	9,673
International [Member]
Segment Reporting Information [Line Items]
Net sales	51,989	42,345	151,694	126,557
Cost of sales	41,317	32,159	119,050	94,652
Gross profit	10,672	10,186	32,644	31,905
Segment depreciation expense	436	317	1,249	791
Segment Profit (Loss)	11,108	10,503	33,893	32,696
Other Segments [Member]
Segment Reporting Information [Line Items]
Net sales	1,079	1,297	3,110	4,056
Cost of sales	1,023	1,221	2,937	4,703
Gross profit	56	76	173	(647)
Segment depreciation expense	66	74	195	570
Segment Profit (Loss)	$ 122	$ 150	$ 368	$ (77)