Purchase contract invalid??

The car of my wife is for sale, unfortunately the car had an accident last year, but was repaired by the dealer again professionally. Now I want to advertise the car, to my knowledge I do not have to point out the accident damage, but only at the buyer’s request. So if I find a buyer who buys the car without demand for accident-free, then let the car check in in a workshop d this then finds that the car had an accident, can he then put the car back on the yard under recovery of the purchase price? To my knowledge, the possibility of conversion with private sale applies two weeks. Only after that the purchase contract is valid.