The two best candidates are, in fact, the buyer and a "third party," the existing mortgage company will tell you to go to Helen Waite.
These would, of course, be unsecured loans, meaning that the lender was taking it on faith that the once-underwater Seller would make good on the note.
The thing to note is that it's not a "short sale" just because the Seller owes more than the buyer's willing to pay. If the Seller can bring money to the table, there's no need for bank approval, it's a straight-up deal.
A short sale has less negative impact on the Seller than a foreclosure would.
I would recommend that you consult an attorney experienced in short sales to expedite the transaction. A loan of the type you are suggesting would be unsecured, so in my opinion very unlikely.
I would strongly recommend hiring experienced professionals for these types of transactions. The attorney and or Realtor can help a lot with paperwork and advice. The Realtor is usually compensated by the bank.
Let me know if I can help with any questions that you may have.
All the best!