Just from personal experience in having to evict tenants in NYC, I am going to assume that the legal process in your situation is the same as for Landlord/Tenant. Unless they leave of their own volition or with a payout, you are banking on 6-9 months of court time and the leniency that is typical in NY for Tenants. And my experience was with tenants who had no lease in place and still it took this much time. Just because you are the new owner of this house does not make a difference. And if they have small children, the court really dishes the dirt your way.
The other major concern is the condition that your "new" home will be in after they leave. Yikes! Though you may be the owner, you do not have any right to enter the premises unless they let you in. Count on repairs when they leave and false claims for injury while on your property.
I would not continue with the purchase unless they are OUT. It is the seller's responsibility; and if it is a bank owned property, either the bank or the listing agent always pays them to leave.
You need an attorney which specializes in Landlord/Tenant law, but I would not even go that far. I would just get my deposit back and walk away. The aggravation and frustration in dealing with a miserable trespasser {oops, I mean tenant} along with his best pal, the Landlord/Tenant Court in NYC, is a NIGHTMARE!
