I looked in the Filing Cabinet and didn't lock onto my answer. That could be because it's a foolish question. But here goes:
Usually, the hairs for the Polyjuice Potion are plucked from somebody's head; this person, judging by Mad-Eye in Goblet, has to be alive. So, do the hairs have to be plucked from a living person at that moment? Hermione got hers from M. Bulstrode's robes; she snatched the wtong ones, Can the hairs of a person be collected from a hairbrush, or a comb or something else? Would it still work because the dead cells are technically no longer growing?