If preservation of the income stream is a primary goal, then a buyer who wishes to assume the defaulted loan should be very attractive to a lender.
The first question you should ask all lenders is, “Subject to underwriting conditions to make sure I am creditworthy, is it possible to assume the loan?”
Unfortunately, many lenders will tell you that assumption is not possible. That may be because it is not allowed under their various contracts with other parties. It might be that assumption is not allowed at that particular stage of default.
For example, the people in customer service who deal with current loans or those less than 60 days past due may not know anything about loan assumptions. At that stage, it might not be allowed. But, if the loan becomes 60, 90, or 120 days past due, there may be different rules.
If you are not happy with the answer you receive, always ask for a second opinion from a supervisor. Also, be sure to ask the supervisor if there will be different rules at a later stage in the default.