It varies by state. There's a list at https://www.nolo.com/legal-encyclopedia/bankruptcy-exemption.... Basically you can keep stuff like the house you live in, your not-flashy car, household goods, tools of your trade, a small amount of personal property (if you own, say, a nice musical instrument or some jewelry worth $2k or whatever). As a general rule, anyone rich enough to have to sell property in a bankruptcy already has health insurance.

And please don't take any of this as a defense of the current abominable US system. I lost my dad to complications of untreated diabetes because he didn't have health insurance. What I'm saying is that people who should declare bankruptcy often don't, because they think bankruptcy will ruin their life. It won't. It protects you from predatory lenders and gives you a fresh start.