There is an enemy off the screen in my game, I shot him in the eye and he ran away. Now whenever I'm in this area all I can do is combat because this person still is there. Is there a way to kill this guy?
EDIT: Read my last post if you want a thorough solution to this problem.

If you have followers, just initiate combat, let them run off-screen and kill the guy. If this is Fallout 2, you might have to set them to hostile combat mode for that.
You yourself can not kill him, no.

How do I let my follower initiate combat? She's standing at one place only, she's not even following me between the turns.
And yes, we're talking about Fallout 1 here.
Edit: I figured it, this however crashes my game!

Well, combat is initiated automatically, right? If so, you should just skip your turn (space) and the follower should attack from his/her own volition.
Though if she (Tandi?) doesn't move at all, ever, that doesn't sound right.
EDIT:
Wah-huh? What happens exactly?

When I press space bar my party member wanders off to the guy, but in two turns the game will crash (Likely when she reaches him).

Well that's a new one. Can't think of a solution to that one off the bat so here's another approach: Fallout NPCs only initiate combat if you're pretty close to them. Have you tried moving away as far as you can in one or two turns (before it crashes obviously) and then ending combat?

I've tried moving to the other end of town even, if I walk away by using all my AP the party member doesn't move and after awhile actually walks back. Even at the other side of the area combat is still initiated (And if I look at my motion sensor, the enemy is pretty far away from the border too)
Thanks, I will try that.
EDIT: I tried the high res pack and set the borders to ignore, but according to my motion sensor the guy ran farther than what this map allows.

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One that might be worth a shot (apart from using an earlier save, which is what I would've done :)) leave town and travel somewhere else, this *might* make the enemy end up inside the town again when you return. (I have seen it happen after doing this with the slavers in FO 2 that has run away, but maybe I've just been lucky when it has happened...)
The travel doesn't have to be very long, just go out a square or two from the town and then return. (and hope it works, like I do that it will for you :))
As soon as he sees you, you'll go into combat mode, but this time you may be able to kill him, if not, do not move, when he's out of your weapons reach just stand still and hit the spacebar. (there's a risk that the NPC won't start to chase after unless you get a hit on the enemy though)

Going in and out didn't fix it, it only helped for one other enemy who didn't get away that far yet.
To give you an impression of how far-off this enemy is, see the attached image. Yellow arrow marks the enemy.
EDIT: I found this ignore_scroll_limits option and now I can see him! But when I approach him he runs off further from the map. He's too far to be sniped down either.
EDIT 2: Finally killed him! I walked as close as I could and then tried to shoot him from a distance with my sniper rifle. Took awhile (22% body hit). Luckily he was almost dead. Thank you guys for helping. Really weird that they let enemies walk off the map.
Final solution:
Get the high-res pack, set IGNORE_MAP_EDGES and IGNORE_PLAYER_SCROLL_LIMITS to 1 in the f1_res.ini, get into the area, walk as close as possible without having him run further and shoot. All that rests that is lucky random rolls (Or unlucky critical misses).