Is this home in New York? You must have an attorney to purchase a home in New York State.. you should always use your own attorney not the sellers! What does your attorney say?
Being that you are in NY, I'm assuming you have an attorney involved in this transaction. You are in contract and your attorney hasn't pulled the c.o.s? He should (and so can you) go to the building department (I've done it over the phone, but if you go you can get copies) and ask if there are c.o.s for all the work done. If not, the bank may not give you a mortgage, and you will just have to make a decision whether or not you want to move ahead without having the owner remedy the situation. Depending on how extensive his non permit renovations were, you could be taking on a real headache. Find out what you're getting into first by checking out the c.o.s.
Just as a p.s., whenever I list a house I make sure I have copies of all the c.o.s at the time I list it, so that when we have an accepted offer I can send them to the buyer and seller's attorneys. I also call or visit the building department to make sure anything I see has a c.o. One of my clients is not in the process of getting a c.o. for a patio that has an open permit but never had a final inspection for a c.o. This could have held up the closing when we find a buyer. In my opinion, this is part of the job, and this agent should have done the same.
We are sorry about this difficulty.
We would recommend that you do two things immediately:
1. contact an attorney for their input on the situation
2. contact the city code enforcement department and explain your situation. It will be important to determine how the illegel renovations could impact you as the new owner, from their perspective.