Maybe I just couldn't find the right path, but I swear you had to fight one on 12F, though I felt like it was reasonable to kill it with a naturally leveled team. (And if you can't kill it, how are you going to kill the stratum boss anyway?)
But yeah, in general, surviving FOEs should be a non-concern because you shouldn't be fighting them unless you know you can kill them, or you're bored, have recently saved, and are fully aware of the risks. Also, be aware of your surroundings. If you run into a random battle around a FOE (especially one that can be aggro'd), just run unless you can clear the battle on the first turn, since each turn in battle counts as a unit of time on the map and it gives the FOE time to ambush you in battle. Additionally, turn off the autopilot if you're in a battle with a FOE. It sounds like it wouldn't matter, but if you run and immediately autopilot back onto the same space, you'll be fighting them again.