It is said that fingernails, toenails and even hair continue to grow even after a person is dead. In films you occasionally see an exhumed corpse with fingernails that are centimetres long. But if the body is dead and thus no longer functional, how can it be that the nails still continue to grow?

Of course it makes no sense. Cell growth requires glucose and oxygen, both of which no longer enter the organism after death. When the body is dead, there is no more cell division and therefore no more cell growth. 

The rumour that fingernails continue to grow after death comes from the fact that the skin on the corpse dries out and recedes from the fingernails and hair. This gives the visual impression that the hair and nails are longer than before.