A lot of that money is in shares of his company, stock options, investments, etc. It's not cash. It's not like he has a giant money bin like Scrooge McDuck full of gold and people will be like "what do we do now?"

Also billionaires die all the time. And any number of things can happen with the wealth they leave behind. Often the shares get bought back or divested. Over time the family's personal stake in the company often diminishes sometimes down to basically nothing. The Walt Disney Company is a good example where the Disney family really no longer has any real stake or major influence.

Wealth often just passes down in some form to next of kin but it doesn't always happen that way. Many people have famously not left their fortunes to their children and instead given it to charity or bankrolled other companies (or governments). The US in general doesn't have a ton of multi generational super wealth especially if the younger generations don't really do anything to keep up the wealth or the mechanism that created the wealth. Today's Carnegies, Rockefeller's, Duponts and Vanderbilt's still have some decent money but it's a rounding error compared to their great grandparents. John D Rockefeller's personal wealth in the late 1800s was $900 million or $24 billion in today's dollars. That being said people like Elon have so much personal wealth, literally more than many countries entire GDPs, that we are in somewhat uncharted waters. I'm actually not sure what would happen with Elon's $191 billion.