Yes, they can sue you. The lender could do either of the following instead of simply accepting the home (e.g. after foreclosure, after you walk away from the home) as payment or satisfaction in full of the debt:1) The could choose to not foreclose (e.g. they feel the home is not worth much) and simpy sue you for the whole amount you owe--foreclosure is an option for the lender, but they are not required to do it.2) They could foreclose, sell the home at foreclosure auction or sheriff's sale, then--if it brings in less than the full remaining balance on the loan--sue you for the remaining, unpaid balance (this is called seeking a "deficiency judgment").