Some enemies like to run away briefly, before coming back. Others might get feared, and run off screen.
Of course, there is also the Treasure Goblins. They try and run from you the moment you start doing damage to them.
I have not seen any evidence that the Treasure Goblins running off screen make other enemies come towards you, but that's a bit hard for me to test because when that happens, I'm usually close on the heels of that goblin, anyway.
Can enemies that you've aggroed run into other enemies you haven't encountered yet, and cause them to aggro against you?