My name is Angie Perez. I represent a number for clients, short sale clients. John is right below. What you are describing is a short sale.
A short sale is simply a situation in which a seller is unable to bring sufficient liquid assets to the closing table to satisfy all liens against real property, including the real estate transfer tax in NJ, real estate commission, legal fees, etc.
This is what we agents in the business call a short sale. A seller who is interested in selling their home short will need to get an approval from all lien holders to sell the home for less than what you owe. In which case, the difference between the sales price versus the amount owed could be package as an unsecured note or the difference can be forgiven.
Debt that is forgiven can be subject to income taxes, which you should consult a CPA to determine how a short sale can affect your taxable income.
Here's a good example of a short sale situation. I represented the seller of a 3 family investment property. My client did not live in the property and he was 9 months behind on payments before he decided to apply for a short sale. Because the home was not his primary residence and he owned more than one home, he was required to hold a small note of $10,000 in which case he makes monthly payments of $100 each month for the next 10 years until the balance is paid off interests free.
You might ask yourself why anyone would want to short sale. In my former client's case, he did not want the stress of managing the property nor foreclosure on his credit report. So, he agreed to the note. Everyone's short sale situation is different. The most important thing to remember I to a. consult a real estate attorney, one familiar with short sales. And b. speak to a short sale specialist like me or someone else and get an assessment of your situation and the value of your home.