You won't achieve luxurious locks or manicured fingernails upon death.
A persistent myth states that all sorts of biological functions occur for days or even months after death. There's some truth to that. Think about the fact that for an organ transplant to occur, the organ can't immediately and utterly fail. Instead, the cells can thrive for hours after the more profound expiration of life.
Glucose ceases to be produced upon death, however, which does affect some new cell growth. That means that fingernails and hair -- which rely on glucose for production -- stop growing pretty much immediately [source: Hammond].
But do know this: Because the skin retracts when dehydrated, it can absolutely appear that the fingernails are longer on a dead person or that more visible stubble is present, looking, for all intents and purposes, that hair and nails have been growing all along.