The rich person would still have other assets worth money. She would still have a house. She would still have a (high paying) job. And she would still have connections to aid her in rebuilding.

The true test would be to take absolutely everything from the rich person and cut them off from all the people who helped them become rich. You can't take away their knowledge and experience so they would still presumably have a large advantage over the poor person. But at least they'd have to walk (not crawl) back to the top.