It depends on the “laws” or traditions of primogeniture of that particular country/state/tribe. And it can also be political. I suggest you might be thinking of noble inheritances.
They don’t literally die out but if it happens that the tradition indicates that the next in line has to be from someone from a distant line, then that “line of inheritance” is figuratively dead. For example if the rules are that only living male sons inherit etc and the current generation who have no sons might have to go back a few generations to identify the inheritor. In the case of rather complex intermarriages and multiple inheritances, there may be challenges to who is legitimate etc.
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