I'm unconvinced rich person net worth is ever actually the dollar figure that's quoted. So much of net worth is in relatively non-liquid assets. If Musk suddenly became a good person and decided to cash out in order to house the homeless, I doubt he would actually end up with $378k per homeless person.

The question is how many new homeless people will be created once he starts doing this? And how much will the price of the average rental go up?

Only if he could barter Tesla stock for the apartments, or by liquidating very very slowly, so as to not crash the value of the rest of his shares (so he can keep doing this). Unfortunately, neither are very realistic (ignoring, of course, that Musk would never do this in the first place).

There's some aspect of housing that's a positional good. There's only so much land in Manhattan, for instance. However, if refugee-camp conditions (ie. a basic place to live but with poor/no economic prospects nearby) are acceptable, it can probably be done with enough musk level wealth.