Running a 12v fridge and protecting the battery from low voltage
What you want to implement is called deep discharge protection for battery. You could find a simple cutoff relay over the internet or build such switch using a Microcontroller which can monitor 'battery's charge status with much higher accuracy. A good way to do this is by measuring both voltage of battery terminals and current. With this peice of information you could esitmate battery's internal resistance that is generally better correlated with depth of discharge.
The key challenge with estimating battery's charge status only by looking at voltage is the fact that terminal voltage is strongly varies greatly depending on the connected load. If a power hungry device draws a lot of current(e.g start of a compressor/motor), the battery's terminal voltage could instantly dip to a pretty low value and eventually recover. While the voltage dropped this does not mean the battery was fully discharged and would cause a false alarm/activation of your relay.
Additionally the device you would use to cutoff battery must implement some form of a voltage hysteresis. Think of it this way, Let's say your battery's voltage dropped to 10v and your circuit cutts off all load, as early as you cuttoff the load the voltage would jump back to 11v, the load would power on again, eventually your load would just keeps turning off/on repeatedly possibly causing more harm to the device you are powering.
Hope this helps.