11 USA states have Non-Recourse mortgages where you also are "not on the hook for a single penny."

Some of those are for purchase and not refinance, but the reality is in almost all states (even those that are not single-action by statute, where single-action is "they can go after you, or the house, but not both") are practically single-action.

In fact, they'd much rather single-action foreclose as they'll likely get a house than force you into bankruptcy where they might not even get that.