I have occasionally pondered as a sci-fi concept a religious cult that dedicates itself to identifying and murdering immortals. In a world where humans have eliminated the natural causes of death, the stability of social systems may demand that unnatural causes of death replace them.
There are other possible structures designed to handle immortals.
These include prohibitions on persons older than N years voting, holding elected office, working in management positions, or controlling property. Which is to say that immortals would be prohibited from directly enforcing their will on younger people, once they get past a certain age. They would then be forced to be sneaky about it, by doing it through art. This substitutes political death for biological death, but also creates an entirely new category of crimes, based on youth fraud.
Then there's the idea that immortals all eventually join the diaspora, and never impact the baseline human culture, because everyone past a statistical age threshold boards a ship bound for distant stars, and is never seen or heard from again, except by those in their ship. Each ship is then expected to evolve its own unique culture, which will likely include some with features that are not destabilized by immortal-versus-mortal tensions. This works out fine until ships start returning, perhaps without reliable knowledge of Earth.
We already have plenty of speculation on this, in the form of vampire novels. In general, the older a vampire character gets, the richer and more callous it becomes. Its life in fiction usually becomes a routine depredation upon mortals, combined with a vicious power struggle among the other immortals. I would imagine a 400-year-old trillionaire to be similar in character.