...Like ChevyThunder mentioned, ...you need to have that car's VIN checked out before you go much further.
...With that said, (I live in NY too) I recently (within the last year) picked up a '67 that had a 'lost registration'. As I'm sure you know, ...cars before '73 have no titles in NY, ...it's the "transferrable" half of the registration that is signed to transfer ownership. Anyway the guy didn't have it, ...and to make a long story short, ...I went to DMV,got all the necessary forms they said I would need, ...and then went to buy the car. I had him sign all the necessary forms and got a bill of sale for the car.
Granted what I was buying was a rusted out, inoperable ($1000) car, not worth a whole lot, ...and NOT something that was a good 'candidate' to be a frauded type of vehicle. (If you're looking at a running driving car and it has the wrong VIN, etc., ...that's a bit of a different story).
Bottom line, ...if the VIN is clean, ...with a little effort you can get the paperwork in order.
Kevin