In a short sale transaction, most lenders will require the seller to sign an arms length affidavit. This is to prevent the buyer from turning around and selling or deeding the property back to a relative or known associate after closing, and to prevent mortgage fraud.
It has been known that sometimes sellers make side deals with a buyer, and once the transaction closes, the buyer transfers the title back to the seller. In this scenario, the seller has re-purchased their own home for less than what they may have previously paid, which then becomes a benefit to the seller, which is not allowed in short sale transactions.
In the arms length transaction document, it generally states that none of the parties involved in the transaction are related, that they can not be family members, business associates, or a person who shares a business interest with the seller. It should also state that there are no hidden terms or arrangements between the buyer, seller and their agents (such as money, kickbacks, move-back in arrangements, putting kids name on leases/deeds, etc.). The seller should not profit or benefit from the short sale.
The essence of the short sale is that the lender has agreed to accept less than what is owed on the property, and therefore sale short. In exchange, the homeowner avoids foreclosure and may have the balance of their debt forgiven.
For specific questions, check with your lender or broker regarding guidelines and policies on short sale transactions.