As you are probably, aware some people make their Tzitzis with 2 holes on each corner to put the Tzitzis through them.
Now, if the Tzitzis get yanked off and we’re left with one big hole, is it a problem to just sew up in the center of the whole and restring new Tzitzis which will, basically, be only hanging on the new thread which will not even be wool?
There is no problem doing that. Since most of the cloth is of wool it is considered a garment of wool, even though there a thread of cotton string sewn into it. We don’t look at the actual thread the tzitzis are hanging from rather the garment as a whole.
When replacing the tzitzis, you have to untie them and restring them on, and not to just sew the corner back on, because t is ta’aseh v’loi min ha’asui.
O:CH 9-1 M:B Biur Halacha D:H Elo. Chayei Adam 11-28, 29.