Is there a term for not being able to pay your mortgage(s)? Like "personal bankruptcy", "consumer default" or something like that?
Not paying a mortgage is first known as delinquency (when payments are missed) and later, default (when the loan is written down and the lender seeks foreclosure). But an inability to pay has no particular term of art attached to it, because an inability to pay can arise either out of illiquidity (debts exceed liquid assets) or insolvency (debts exceed liquid assets and ability to borrow against future income).
Insolvent household, maybe? For a person or a household, the most common term is insolvency.