It depends on your agreements. I imagine that they have a clause in those documents that speaks exactly to this issue and allows them a right to rescind the transaction.
So review all the documents, contact the auto dealer so they can state explicitly the contractual basis for this demand, and then, maybe, speak with an attorney.
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Did you make any assertions as to accident history of the car ? Did you complete a form declaring your knowledge about the history ? If the accident happened while you owned the car, and you made assertions that it had a clean history, it is more likely that they can come after you and returning the car will likely be the best solution. Plus consider what you signed as the prior answer provided, since it will likely control many of the other scenarios.
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Mr. Murillo is directly on point. The contractual agreements that you sign will have provisions exactly about this issue. The auto dealer is probably stating that you either made a material misrepresentation about the car that you were trading in or failed in "good faith" to make a disclosure of the prior accident and it being considered a total loss. The paperwork should let you know if the inspection that they conducted waived their right to object at a later date. Good luck
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