Okay, so I made it out to the rest of the map. I was wandering around, and killed the "get out" monster … except that even after it hit 0, I was still in battle for at least 3 turns. So I sat around recovering and occasionally hitting it… which eventually led to a game over. I'm thinking … that's not how this is supposed to go.
Also, and I don't know how easy this is to fix, but sometimes Illyana will attack something after it's dead -- for example, using a triple attack on two monsters, but slashing the first one twice, killing it on the first blow, and then hitting the second monster only once. I'm not sure how intelligently this bit of battle can be coded from your end, but it looks really weird for the end-user.
The issue with Illyana is something I do plan to fix sometime soon. As far as the get out monster, I wanted to lock that part of the game off to a player until they advanced enough in the story to access that area. It was a fun creative way to do so. Making an enemy that isn't killable, but also doesn't attack. The music chosen for that fight and the fact even at 0 health it doesn't die should be a sign to run as it's an unwinnable fight. My playtesters, to my surprise kept fighting it, thinking there would be something that would happen. An easteregg of sorts. Nothing was planned like that for this fight, but due to several people expecting something like that, I added in something special. A one hit kill move easter egg. Granted you'd have to be fighting it for a long while for this to happen. I recommend just running from it until you reach the point you can access that area.