First.... I am sorry you are loosing your home.
I do not know a single bank that will allow this. They generally make you sign arms length transaction meaning you are not related to the person whom is purchasing the home. I have seen banks refuse to sell if the investor was going to rent back the the original owner which in my opinion is going a bit too far but the banks are not happy campers when it comes to this.
Metlife Home loans
I have had many cases where when a relative came up with a reasonable settlement amount the bank has taken it, you need to avoid having the bank think it is your money and you will need proof that your relative has the money in full.
Buy a home after foreclosure expert
You'll have to sell for the full amount of the mortgage plus any penalties and other fees. But if you can sell for what you owe, then you can sell to anyone you want.
If you want to sell for less than you owe, then you're talking about a short sale. And your lender would have to approve it.
Hope that helps.