I hear the shaila but I don’t chap why you’re saying that the guy becomes a shoel on the car. Either way this case is l’fum rihata a mefureshe mishna (Bava Kama 47a):
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If when the guy brings it birshus the ba’al hachatzer is chayav then obviously when the ba’al hachatzer’s own stuff gets damaged it’s his own loss. L’mayseh I still hear a shaila because it could be if the bag was closed the ba’al ha-car isn’t expected to assume it’s something like chicken that can easily spoil. Or maybe it’s his achrayus to know, especially on Friday when everyone has chicken in their bags. Good shaila.