Legal Question in Credit and Debt Law in California

It depends on the equity in your house. A certain dollar amount of equity is protected by homestead and you don't have to record a declaration of homestead in order to claim the exemption - it is automatic. If there is equity over and above any mortgage balance plus the homestead exemption (the amount of the exemption varies depending on your age and other personal circumstances) then, yes, they could get a judgment against you and have your house sold under a writ of execution. Your mortgage lender would then be paid out of the sale, you would get the homestead exemption amount, and the credit card company would get the rest - up to the amount of the debt, plus fees and costs. If there was anything left after that, you would get it.