You could own a room in a crack-house

If you’re injured, or have a lawyer and doctor say you were, yeah… you don’t literally get their house but they might have to sell it to pay you. More often, their insurance company would pay.

You probably wouldnt have gotten the house. Rather he'd have to sell it to pay the debt.

someone without insurance rear-ended my vehicle but I chose not to pursue it because then my own insurance rates would've gone up.

Somehow, this sounds deeply wrong. Your insurance should cover you regardless of what happens. If it’s an act of god, the insurance company should just swallow those costs. If it’s caused by a third party who is not their customer, they should go after the company that insured the other party, or the other party directly if uninsured.

No matter what the circumstances, if you are not at fault you should never see an increase in your rates, no matter how catastrophic the damage or the costs to make it right.