Is removing something sticky from a garment, such as a feminine napkin from underwear, a violation of potzayah if when doing so threads are being pulled out?

Shalom, Thank you for your question. The first issue that comes to mind with your question is one of "koraya" or tearing. However, in this case it would certainly be permitted for two main reasons. Firstly, the hygienic napkin is stuck on with intent (and reality) that it is temporary. Just as closing and oping a zipper of a jacket is not a violation of "sewing" and "tearing", because the join created by the zipper is intended to be undone and non-permanent, so here to, the napkin is "stuck" in place with the intent that it be removed after a few hours. As to "potzayah", there is much discussion as to exactly what is included in this labor. It is true that pulling out loose threads from a garment may be included in this, and one should be careful to refrain from doing so. However, in your case this would not apply. This is because of two factors that come together – firstly, you have no intent when removing the napkin to remove threads from the garment. Secondly, it is not inevitable that threads will always be pulled out. When we have an unintentional act, coupled with the fact that the forbidden result is not inevitable, it is permitted on Shabbat. For example, one may walk across a lawn, even though there is a chance (even greater than 50%) that one may pull out grass with their shoes or feet. This is because one does not intend to pull out the grass, and it is not inevitable that the grass will be pulled out. (Of course if one really wanted to get rid of a weed and walked over it on purpose so that it would, hopefully, come out, it would be forbidden. Also, even if someone didn't want to cut the grass, but was wearing shoes that had blades on them [some type of crazy lawn mowing shoes !] it would also be forbidden). In short – you may remove such hygienic napkins from your garments on Shabbat. Blessings.