My friend remembers only scene, in which immortal people are after radiation. They are probably gray or silver (I think about color of their skin), they are bald completely and hidden in caves. They are reached by people from the top of the planet who have become immune to radiation or survived it. A scene similar to “Planet of the Apes”, because they meet these old people in the underground.
It isn’t “Time Machine” (1960), although Morlocks are some similar, but they aren’t bald. 