yes,they can,claim the car back,they still own it. did you do a HPI check on the car when you bought it, the dealer who sold it to you should have done it when he bought it as well.i would think you have a claim against the dealer who sold it to you,we had the very same thing happen to us,we sold a car with finance owing on it,and we should have checked,it wasent a lot of money,about �800,but we had to pay it off,or we would have been in trouble.but lease cars are different,i would see a solicitor if i were you,or try and sort out with the finance company,some sort of solution.