Why not? You have the option to run away from a mob, and regenerate your HP as well. It's only fair! :P
Yes, it's normal. Mobs can/will run away sometimes. Any idle mob usually regenerates HP. Can't count how many events I've been in, where the group wipes, and we watch the mob regain HP while we try to recover. It happens.
FFXI - LordDVS <Bismarck> BLU75 DRK75 SAM75 BST75 PLD75