So, a good fridge will have an automatic shutoff that will turn off the fridge if the voltage dropped too low. Most of the time you wire a fridge directly to the battery anyways.
Hey mate, would you be able to share with us what unit your are running for this kind of set up? I'm currently looking at options to do exactly this.I just use a 25ah lithium power pack (kickass I think). It will run my 50l fridge for about 13 hrs. Uses the car 12v whilst running and I’ve got a 50W solar blanket for when it’s not. The blanket can fully recharge the power pack whilst running the fridge during the day while stopped. $450 for the power pack and solar blanket all up. And totally portable