There isn't a specific answer to this question, it depends on a few variables. The bank is going to assess how much is still owed on the mortgage, the current market value of the house, and the cost of foreclosing and reselling the house.

If you owe less than the house is worth, the bank has no real incentive to reduce the principle balance because they will make their money back when the house sells.

If you owe quite a bit more than the current market value of the house, then it is in their favor to reduce the balance. They can only sell the house for the market value anyway, plus the cost and hassle of foreclosing, listing the house etc. so you are much more likely to get a reduction.

If the balance and the value of the house are about the same, it can go either way depending on the neighborhood the house is in (is it desirable and easy to sell a house in, are there a lot of other homes for sale in the area, etc.). Usually the bank doesn't want to lower the principle balance, since that is money they already paid out. They typically are much more willing to reduce your APR, either temporarily or permanently. The one thing to watch out for is sometimes they will increase the terms of the loan. A reduction in balance or interest rate isn't a bargain if you have to make 10 more years of payments. They will get all of the money you 'saved' back over the course of the extended loan.

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