In a perfect world, the answer would be yes. A family member helping you out in this horrible real estate market and economic crisis. Unfortunately, the lenders do not see it that way. It is a type of straw sale that is highly suspect and sometimes illegal. If you can't make your mortgage payments, a family member could help you, according to the lenders. Otherwise, you give back the home. In a short sale, a home owner is trying to avoid foreclosure, and in many instances, if not most, the lenders make you sign a host of legal documents, waivers and affidavits stating precisely that you are not selling to a family member, that you are not residing in the new purchaser's home, and other disclaimers, specifially designed to protect them and be able to come after you in the event that you were dishonest. Be wary of these type of transactions and if a family member does want your house becasue it is a good deal or to assist you, be sure to advise the lender's representatives of this connection, or it could come back to bite you.
There is no law of any kind regarding short sales or who or who can't purchase at short sale, or who can live there, or whether a short sale buyer can then resell the property. However, many of the mortgage companies try to impose the condition that it be an "arms' length transaction", meaning that there is no relationship between the buyer and seller. As part of many (maybe all) short sales, they require a sworn affidavit to that effect. If there is any obvious connection between the seller and the buyer (same last name, same address, etc.) they will refuse to agree to the short sale.
You may well ask why they care who the buyer is, assuming the price is agreeable. There is a major misunderstanding that the mortgage companies deliberately try to cause, giving borrowers and the world in general the idea that the mortgage companies are interested in "helping" borrowers out of a jam. What they are interested in doing is helping themselves and their clients (the real owners of the loans). They don't want to participate in what are really "self-help" modifications or refinances, where the principal is effectively reduced to fair market value, where a borrower makes a short sale to a related party or friend, who then makes it available to the borrower after the short sale on a rental or some other basis. Assuming the former borrower is able to file bankruptcy and so to discharge the deficiency liability, this of course then takes the heat off the borrower and allows them the use of their house at a reasonable cost. The very fact that the mortgage companies attempt to prevent this is proof (assuming anyone still needs proof) that your mortgage company is NOT there to help you.
From what I hear from clients and prospective clients, people who could have done exactly that - an "inside" short sale and are are completely satisfied with that outcome and no doubt most will get away with it. IF the mortgage company ever found out that the parties to the short sale swore untruthfully that they are not related parties, the mortgage company would, at least in theory, have the foundation of a suit for fraud against them. However, it would be interesting to know what damages they would be able to prove if this were to ever happen, since presumably the price they approved would be what they felt to be fair market value anyway. Their only "damages" would be the escape of the borrower from their clutches on a reasonable basis.