OK, there are few local private NY and NJ dealers that sell super cheap cars. Usually, they are in an accident and rebuilt title. I bet if you pull the carfax it will show some accident. If carfax comes clean. I would seriously get this looked at by trusted shop.
edit: Also majority of this dealers are super shady and comes with bad reviews. Just do a simple search on their history. Avoid and save up and buy something more legit.
Look at the
CL ad: You must have a 780+ credit score to be qualified for advertisement Price.