Bones do not reanimate, but when butchering in reanimating biomes the skin and hair will sometimes reanimate before the dorfs manage to process it (or dispose of it), even if they stand ready to do so immediately. General hair and skin is not invincible, but HEAD hair and skin is (or at least close enough in practice) in regular combat. A reanimated skin can split up into multiple skins when defeated, and they can be reanimated in turn, and one of these can be the dreaded head one. In addition to this, when a defeated reanimated skin splits up, one or more parts can get stuck in the butchery/tannery building, requiring the deconstruction/reconstruction of the building to get it out (and give it extra time to reanimate).
A method that's worked reasonably well is to line the relevant workshops (butchery/tannery/thread processing farmer's workshop) with cage traps and have militia stationed in the area when butchering. Reanimated pieces can be caught in traps, and civilians can dodge into them, which saves them from the reanimated parts, but makes it a pain to get them out, as the cages have to be built, hooked to a lever, and the lever has to be pulled). Invincible reanimated parts in cages can be dealt with by atom smashing, although obsidian casing works as well. There are reports that reanimated parts dumped in magma keeps crawling around at the bottom of the magma sea, although I haven't tried that myself.