The Primary Concern When Conferring Special Abilities Voluntarily

What happens if they don't? Presuming it's a limited kind of thing. For instance, if only person in the world can have the Aldebaran power, what happens if the holder dies without passing it on? Think about it. Maybe a fresh new guy will figure it out a hundred years hence. Maybe the closest survivor gets it. Maybe magic is fading from the world because these morons forget the succession part. Whatever it is, have something.