Also, the amount of the sale will be recorded at the lower price. This will impact the sales value of homes in the area when reviewed by appraisers, etc...
If you are actually - really - purchasing personal property (i.e. furniture, loan mowers, etc...) not included in a real estate contract, that is an entirely different matter. But it doesn't sound like this is the case.
You need to consult with your Realtor or an Attorney. However, if you are purchasing a short sale, you will have to sign paperwork for the seller's bank stating the seller is receiving NO money. The seller is not allowed to receive ANY cash from the buyer in a short sale (since the bank is taking a lose, they want all the money).