They will lose their house. HELOCs are secured by the home, either by a deed of trust or a mortgage, depending on the state.
Under federal law, if the debtor cannot pay the creditor gets the house, and the debtor gets whatever is left over after sale expenses and loan payoff. Court proceedings can delay but cannot cancel the debt. To get out of it, the debtor would have to prove that the lender did not provide certain required disclosures under federal law (rescission, Reg Z), or qualify under various state laws. But the vast majority of people have no valid legal claims.
I believe CA does have a law cancelling overages. I.E., if the person ended up owing more than the house was worth, all the creditor would get was the house. I’ll have to look it up. A couple other states have statutes highly favorable to homeowners in this situation.
Paradoxically, a homeowner in way over their head (more loan than house value) might do better with a second-lien home equity or HELOC. You normally need to be under 10% or so. The creditor might deal because the first mortgagee is going to get almost everything, so it is better to work something out to get more on balance.
