There's really nothing you can do to force the lender to act faster.
You are right that a deficiency judgment may be obtained when a property in foreclosure is sold at a public sale for less than the loan amount which the underlying mortgage secures. These judgments are limited to the difference between the fair market value of the property (regardless of what the property sold for at the foreclosure sale) and the defaulted loan amount at the time of sale. Fair market value is determined by appraisal.
It is possible that the lender is waiting on property values to increase, but it has that right. The flip side is that the higher the market value, the more the property will sell for, thereby decreasing your exposure for a deficiency.
Interest is growing on your unpaid balance, yes. Also, if you're in default, the lender has a right to these fees and interest under the mortgage documents, so there's really no way to stop them from accruing.
You're just going to have to take what you signed up for if you defaulted. There's no goo way out of this if the lender will not accept a deed in lieu.
Filing bankruptcy will get rid of a deficiency judgment. However, my suggestion is to wait and see what they're going to do before taking that route, especially if you're current on all other debts.
It may be that the lender will take a deed in lieu of foreclosure at some point in the future, and if that occurs, you wouldn't need to file for bankruptcy.
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