Except you need cash flow or savings to afford a house, even a paid off one. If you don't pay your mortgage or tax bill, then someone is going to evict you.
Houses aren't great protection against homelessness because they don't address the root cause of being homeless: having no money or income. They can provide a buffer because it's harder to foreclose on a person than it is to evict them. While this additional time may certainly make a difference, in all likelihood the outcome of losing a job and not being able to find another one is probably the same.
You can't liquidate any built up equity either, since you probably need income or assets to get a rental or equity loan. So it's completely possible that you lose any built up equity in the event of a foreclosure too.