Can I refuse to inherit a house with an underwater mortgage?

My mother passed away and I inherited a house with a mortgage underwater by nearly 50k. I am the sole heir (mom's husband deceased, parent deceased, no grandparents, siblings, etc). There is a pending cause of action filed by my mother prior to her death, which is now an asset of the estate. There are no other assets in the estate. Question; can I disavow my interest in inheriting the underwater house so that it passes to NY State (by rules of intestacy) without also disavowing the potential payout in the cause of action? We've tried getting the bank to agree to a deed-in-lieu, but they are not being cooperative. We've also considered letting the house foreclose, but don't want thousands of dollars in legal fees slapped against the estate that will inevitably total more than the settlement payout. The estate has no money to pay the bills (mortgage, utilities, upkeep, etc) as I am currently paying out of pocket, and can't continue to do this. I want to preserve my interest in the settlement, but fear that I will loose this interest to the bank simply because I cannot afford to pay the mortgage. Any thoughts would be appreciated?