You can't drop below Level 1.
When you fail to defeat a monster, you have to try to Run Away by rolling a 5 or 6 on the die. If you fail to Run Away, you suffer whatever Bad Stuff is printed on the monster's card.
I encourage you to reread the game rules, particularly the Combat section. We tried to be as clear as we could about what happens during combat and we appreciate feedback on how we can do better.
Have you tried the
Flash demo? It walks you through a couple of turns and shows you the various things that can happen.