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If you cannot refinance this mortgage for a better rate, you don't have a lot of options. Because of the fraudulent transfer act, any transfer of the property you do at this point would be subject to reversal by the creditor. The presumption in these cases is that you transferred the property into a trust or to another person to protect it from creditors - which is illegal. You would have to prove that this is not true. Unfortunately, this is very hard to do.
The best thing to do is offer the lender a deed in lieu of foreclosure. This actually avoids the foreclosure process and also prohibits the lender from seeking a deficiency judgment against you. The catch is that securing a deed in lieu of foreclosure is totally up to the bank, and it will not agree to this unless the lender believes that it can sell the property for at least what is owed on it.
If they won't agree, and the foreclosure sale doesn't generate enough money to satisfy the debt, the lender can seek a deficiency judgment and garnish wages, freeze accounts, place liens on your property, force the sale of your property, etc.