That is a complicated question which requires a careful analysis of YOUR facts, and YOUR priorities. For example, do you have a defense to the foreclosure that can hold up? Adding another $200,000 to the mortgage principal, and that too with a balloon payment sounds like a set up for disaster down the road. You need to talk to a competent attorney knowledgeable in foreclosure defense.
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I agree with Krishnan that depends on your priorities--if you want to keep the home, then taking the loan modification (assuming the monthly payment works for you) is probably the route you should take. The balloon payment arrangement is to structure the loan mod so that the monthly payments are lower. The balloon contains the accrued interest that you weren't paying during the pendency of the foreclosure and whatever other disbursement the banks made during the pendency of the foreclosure (i.e. insurance payment, tax payments, atty fees etc). The alternative to the balloon is recapitalize the $200k into the principal with the result that you would have a much higher monthly payment--perhaps higher than what you were originally paying. Even though you have a balloon payment, the idea is that by the time the balloon payment becomes due (which is probably very many years), you will have had an opportunity to sell the home, refinance, or improve your economic situation.
A consent judgment without deficiency is just allowing the foreclosure to go forward and letting the bank take the house without contest. By not contesting the foreclosure and making the bank's life easy, the bank is saying they will not sue you again personally if the value of the house happens to be less than the mortgage debt. This is a substantial benefit, as it give you an opportunity to be done with the foreclosure, make a clean break and start from scratch. ***Notwithstanding the foregoing***, you need to discuss the details with a competent attorney, and perhaps an accountant if this is an investment property. The sort of decision you have to make is beyond the scope of a quick question and answer on a website.
I'm not a New York attorney, but yikes, that doesn't sound like a good loan modification. Who is offering it to you? Did you apply for a modification under the Making Home Affordable Program (HAMP)? If not, you should probably look into it. A consent foreclosure is not a bad option if you're not interested in staying the property, especially if you don't have to pay a deficiency. If you agree to a consent foreclosure you may still be able to negotiate more time to stay in the property before having to move, or getting some money to help you move. Consult with an attorney in your area if you are having any problems communicating with the bank.
The information in this answer is not intended as legal advice nor do I intend to create an attorney-client relationship with any reader simply by answering this question or contributing as a member of AVVO.