If two people own a home, and one moves out while the house is on the market, does the person who moved out still have to pay?

The bank does not care about the personal problems of the people who sign the note. Under most promissory notes the liability is joint and several, meaning that each partner owes the entire amount, You may have a claim against your partner for your contributions in excess of 50% in a partition case, My advice would be to settle this matter quickly or the equity will go to pay the lawyers.