I never tried to edit the fpe file in order to make a negative movement, but if that's possible (maybe someone else tried it, I haven't so I'm notsure), than it should be pretty easy with the "death" animation. If the player is in zone, then that animation would occur.
The second one, if you alter the state of the zombie if player is within the zone or out of the zone, or at some distance, might work. You can do some tests with this hints, but I better leave it to the scripting masters.
I'm pretty sure I know everything. Doubts are something rare in me and I am never wrong, as this signature can prove.