First, be aware that Carfax is not perfect, so it's possible the loss or damage report is incorrect.If the Carfax report is good, then the issue becomes whether or not there was any fraud in the sale, which depends primarily on whether the dealer knew or reasonably should have known of the former or previous damage. IF the dealer did know, then the dealer may have committed fraud by representing that the car had no negative history. If fraud was committed, then you may able to receive compensation--though you'd have to sue to try to recover it.On the other hand, if there was no misrepresentation or fraud--so, if the dealer did not know of the damage--the dealer would not be liable; i.e. if they told you what they know, they did nothing wrong, and without doing something wrong, there is no liability.