Lenders are all about numbers, so the letter isn't a sob story about the borrower's difficulties. It should be a factual description of a financial situation that is leading up to a bankruptcy or a foreclosure on their home, or both. The lender must be convinced that their only other option is foreclosure, and then they can analyze the numbers to see if a short sale is a preferable alternative.
Different sources quote different numbers, but the average seems to run around $50,000 in costs to the lender for the average foreclosure process. Then there are the reserves that are required to be held to back up non-performing loans. The lender must tie up resources that could be invested elsewhere to back up these loans. So, they are open to alternatives.
The borrower should write the letter in their own words, but they need to make sure that there is a clear picture of their financial condition, and back up their claims to hardship with documentation, such as pay stubs, medical bills, job layoff letters and more. The numbers should clearly illustrate that the borrower is headed for foreclosure or bankruptcy.