was your CONVERTER(CHARGER) on during this time?
if not, or it's breaker was tripped, your FRIDGE and Inverter would then have been running all night on the batteries alone, as well as anything else you used that are 12v, such as lights and fans, etc.
Remember that for small inverters that are dedicated to 'only' the fridge typically are not wired into your Main panel, so if the CHARGER is not charging the battery bank the whole time the Inverter is on, then the batteries are being drawn down with no charging, even if everything else on 120v power works fine, such as the air conditioner(s), and things plugged into any of your wall outlets.
Why would the Chassis(Vehicle) battery have anything to do with this?
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