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Since you mentioned the Fannie Mae mortgage release program, I presume that you have already look for information and you may have seen this: https://www.knowyouroptions.com/avoid-foreclosure/options-to-leave-your-home/mortgage-release
You did not say if you are current on your mortgage or not. Generally, the lenders will not consider programs of any kind for mortgages that are in current status. By way general explanation, the deed in lieu of foreclosure means that you give the house back to the bank and they sell it. You are released from your mortgage loan liability. The alternative is for you to put your home on the market through a local real estate broker and try to obtain the highest possible price. If the best price. You can obtain is less than the mortgage balance. You can submit a request to the mortgage company to accept it. That is called a short sale. The banks prefer that you do a short sale rather than a deed in lieu of foreclosure.Pay particular attention to the requirements for the lender to consider either the deed in lieu or short sale there pretty much the same and they seem to take forever to get worked out. See: https://www.fanniemae.com/content/guide/servicing/d2/3.3/02.html You can see why it takes so long for decisions to be made. It is well known fact that buyers waiting for short sale approval will get frustrated and walk away. Sometimes more than one buyer will do that in any given sale.
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In that case, your best option seems to be to buy the new home first, while your credit is still good, and then deal with the current condo either through a deed in Lieu, short sale, or an outright walk-away. There's no outright answer that will solve the condo problem without some credit damage. You literally have to "go with the flow".
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That's the $64,000 question. They would probably require you to show prospective rental income from it.