Yes, the bank can do that. Generally speaking, mortgage-loan contracts for individuals signed with bank entities include the faculty for the bank being able to choose any of the debtor’s assets, present or future, at the time they recover the debt. Therefore, the bank can proceed against the mortgaged property and also against other assets if the debt is not fully covered by such mortgaged property, and even against those other assets different than the mortgaged property instead of this one.