If you have the same Magnum MS2812 2800 watt PSW inverter/converter we do, it does have some built in protections for overload and over-temp conditions while on shore-power. It will shut itself off if it detects either condition. While on battery-power, it also monitors the batteries for low and high voltage conditions, and will shut itself off to protect itself and your appliances.
To the best of my knowledge, it does not protect against some low voltage conditions - conditions that can occur in RV parks, and which can damage appliances. I also don't think it has an automatic reset delay to protect the AC compressor like some aftermarket power monitors do.
If a shore-power problem causes your inverter to shut off, your AC systems are dead (Like your res-fridge). If you have an in-line power monitor (like the Progressive EMS-PT50C) it will shut the power off to the coach when it detects a problem, leaving you with the ability to run your appliances off your still-functioning inverter. It will also auto-reset when it senses that the power is good again, but only after a built in delay to protect the AC's compressors.
We have the Magnum MS 2812 in our coach (it's a nice system) but even so, I wouldn't hook up to shore-power without our EMS-PT50C. FWIW
Kev
(By the way, welcome to the RVForum Terry!)