Stuck in an Elevator

This next scenario is also another popular movie trope. Someone gets a body part stuck in an elevator door and after it closes, the elevator car starts to ascend. The person’s body part gets stuck and they begin to panic.
It is usually a funny bit in comedies and nothing crazy happens, but horror movies are a different story. In horror movies, someone’s head gets stuck in the doors and they end up decapitated. It seems crazy but if that were to actually happen to someone, would the results be fatal?