The gemara Chulin 20b says that the p'sul of חלדה is similar to a weasel that lives in the holes of houses which is often hidden. There seems to be a machlokes in the gemara there whether it is necessary for the beis ha'shechita to be opened so that the part of the knife that is cutting is visible, or whether it is sufficient for part of the knife to be visible as it is cutting (see rashi d.h. הא מיגליא). Nevertheless, there is a din that the knife cannot be hidden underneath something at the time of the shechita. The gemara asks a series of questions according to Rav who says that even if the knife is hidden underneath the skin of the animal it is a problem, what is the din if it is under a cloth, or under the tangled wool. Rashi explains that even if the skin of the animal creates a problem, that is because it is at least part of the animal, but a foreign object such as a cloth may not be a problem. According to Rashi it isn't clear what the question would be regarding the tangled wool - shouldn't that be exactly like the skin of the animal? the Ran explains that the tangled wool isn't part of the animal, therefore even if a cloth would be a problem, the tangled wool would be less connected to the animal and may not be a problem. However, the Rosh seems to understand that the tangled wool is part of the animal that is going to be sheared - the question is that if skin is a problem, maybe the tangled wool is not a problem, and if the tangled wool is also a problem, the cloth which is a completely foreign object may not be a problem. Either way, the sevara of the Rosh, Ran and Rashi is that the more foreign the object the less likely it is to be a problem of chalada. The Ran and Rosh also seem to agree that even according to the maskana of the gemara leaving with a תיקו that the cloth and wool are indeed a problem, it is only because they are attached or tied onto the animal. However, a cloth that is draped over the animal isn't a problem of chalada.
The Rambam (3:10) concludes from the gemara that even if one spreads a cloth over the knife and the animals neck it is considered chalada - הואיל ואין הסכין גלויה הרי זו ספק נבלה. The Rambam seems to hold that chalada is a din that during the act of shechita the knife must be visible so that anything blocking the knife, even if not attached to the animal could constitute a problem of chalada.
The Mishna L'melech references Rashi in Bechoros 24b. The mishna that says when one is shechting a b'chor they are allowed to detach hair to make a place for the knife and it isn't considered a violation of shearing a b'chor. Rashi explains that the reason it is necessary to make a space for the knife is to avoid chalada. Tosafos asks on Rashi that it can't be for a halachic reason, rather a practical one, because the gemara leaves with a תיקו whether tangled hair creates a problem of chalada - if Rashi is correct that the mishna requires cutting the hair to avoid chalada, the gemara should have proven from the mishna in bechoros that it is a problem. Perhaps Rashi would say that the proof from the mishna isn't muchrach since the peshat could be like tosafos that it was cleared for practical reasons. However, since we pasken that we have to be machmir about chalada by tangled hair due to the teiku that the gemara leaves with, rashi explains the mishna by bechor that one would actually be required to cut the hair to avoid chalada.