Mishnah Berurah — משנה ברורה

That the weaver leaves over - One should not ask [the following question]: That even without this, there is something [that makes it] invalid, for the threads were not spun for the sake of [the mitzvah of] ציצית (ie. the Shulchan Aruch said the reason is because of disgracing the mitzvah, but even without that, we're talking about threads taken from a loom which is used to make a garment, not ציצית strings... so obviously the threads left over on the loom were not made for the sake of the mitzvah). We can answer that we are referring to even where initially the threads were spun for the sake of the [the mitzvah of] ציצית, and afterwards he wove a garment from them, and even in this case they are invalid because of disgracing the mitzvah [Ta"z]. And in Sefer Hamaor, he wrote [that] the reason is because there's a requirement that [the material/fibers used for the ציצית strings that hang off] the corner, be the same material as [what's used for the actual garment of] the corner. And [here] these materials are not fit to make from them a garment since they are the remnants of wool and a garment cannot be made from their [small] quantity... Until here are his words (of the Sefer Hamaor). And if so, any type of wool which is subpar, of which a garment cannot be made from it, is invalid for making ציצית strings [Magen Avraham].