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71
Answer: There are three potential Shabbat prohibitions that need to be addressed: borer (selecting), muktzeh, and koreiah (ripping).
We have discussed in the past (see Living the Halachic Process, vol. IV, C-5) a similar case – removing detached hair from one’s head of hair. We concluded, based on very strong indications but without an outright proof, that this action does not violate borer or muktzeh. We will summarize the main indications.

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Regarding muktzeh, since a detached hair is useless, it is muktzeh machamat gufo. If one removes it with a utensil, then it would be permitted because it is indirect movement (tiltul min hatzad) for the purpose of a permitted item, i.e., the necklace (Shulchan Aruch, OC 311:8). Actually it is permitted to handle directly, as we pointed out that it is permitted to directly touch useless things in removing them from desired utensils, e.g., when cleaning dishes. The Chazon Ish (OC 47:15) explains that in such cases, the impurities being removed are considered subsumed under the non-muktzeh items. While some disagree, the consensus follows the Chazon Ish (see Shemirat Shabbat K’hilchata 14:(149); Orchot Shabbat 19:207). One might claim that if the hair protrudes from the necklace, it is separate and muktzeh, but this is likely incorrect, as comparison to feathers indicates.
Now we relate to ripping the hair to remove it. One might actually prefer to keep it intact to remove the hair in one shot, making ripping, even if forbidden, an example of davar she’eino mitkaven, an unintentional forbidden consequence of one’s actions, which is permitted (Shulchan Aruch, Orach Chayim 337:1). If removal without ripping is impossible, we would have to deal with the laws of p’sik reishei (the forbidden result will definitely occur), which is usually forbidden (ibid.). On the other hand, there are cases (lo nicha lei, d’rabbanan) where some permit even p’sik reishei (see Yabia Omer III, OC 20).
However, this discussion is unnecessary because it is actually permitted to cut a hair in the setting of our discussion. Cutting detached hair is not gozez. If one cuts a loose strand of hair to a purposeful size this would be a violation of mechatech (see Mishna Berura 340:41). (See Be’ur Halacha to OC 340:13 regarding when there would be a prohibition of koreia al m’nat l’taken and when there would be metaken mana). However, when one cuts a flimsy object because it is in the way and the ripped object will not be reused, it is permitted (Shulchan Aruch, OC 314:8 and Be’ur Halacha ad loc.). Admittedly, poskim rule that not only may one not undo a knot, but he may not cut the knot cord at any point (Mishna Berura 317:23). But as hopelessly tangled as a hair might become, that does not automatically make it a halachic knot, and even if it fit the description, it can still be undone or cut when the knot was formed accidentally (ibid.).
In summary, if one feels the need to remove hair(s) from her necklace specifically on Shabbat, it would be permitted to do so by pulling off, ripping off, or cutting the hairs. Once removed, the hair scraps would be muktzeh.

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