You can Short Sell the house if you get approval from both mortgage companies. If you do get approval, you would not be liable for the difference between the sales price and the balance on the mortgages. However, unless you can sell the house for more than what is owed on both mortgages (which is what a Short Sale is), there is no advantage for you to conduct a Short Sale, as the result can easily be that you have to move out sooner.
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