It sounds like you owe more on the house than it's worth, you're not living there, and the bank is offering 1) foreclosure or 2) a deed in lieu of foreclosure, with a note to the bank for the excess debt.
The biggest difference in those alternatives is that with #2, you have a deal to pay the bank what you owe, and with #1, they'll sue you for the difference instead, plus the costs of the foreclosure and the suit. If you have not non-exempt assets, and are not concerned about your credit, maybe the suit doesn't make a lot of difference to you. Otherwise, you're better off to take option #1.
The repercussion under the current offer is that you will still owe the bank the difference between the value of the house and the loan. You should talk to the bank about giving them a deed in lieu of foreclosure and having them write off any balance due on the note. Or, you should try to get them to agree to a short sale where you sell the house for less than the note and the bank forgiveness the rest of your debt to them. An attorney may be helpful negotiating one of those alternatives for you.
You should retain an attorney to review the documents you and the bank signed. It may be that the bank has breached an agreement to lend money or to carry a mortgage or in some other way. What the documents state is important. Based on the documents, or just the situation in general, you may be able to negotiate your way out of the problem, with some savvy legal advice. The presence of an attorney could make the bank fearful of litigation as it seems that not all is on the up and up with the bank, and you may be able to extract a better deal. You do not want this incident to damage your credit if you can avoid doing so. So, you need to be careful how the bank styles the resolution so that the bank does not turn into a credit reporting agency any negative credit history for you.