If the lender forgives the remaining debt, it should (but may neglect to) issue a 1099-C. The IRS views forgiven debt as taxable income... with some exceptions.

If the mortgaged property was your principal residence, you may find all, or some of the forgiven debt exempt from tax. It depends upon the amount of your acquisition indebtedness.... the amount of the purchase money mortgage you used to finance the purchase of the property. If you refinanced the original mortgage... or if you took out a second mortgage... you may have a tax consequence.

If the lender neglects to issue a 1099-C, you, as taxpayer, still have a duty to report and treat the income.