Back to the OP, a AvP 1 and 2 had sections where you played as the predator or and alien, and were similar.... Civies would cringe and stuff.
Don't forget Manhunt, either
Having unarmed characters in a FPS that are scared of your heavily armed character barging in, and shooting up the place isn't quite the same thing. Neither is hunting down crazy gangsters who're trying to hunt you down themselves.
My idea was that you could play as either a victim or the killer, you could procedurally generate pretty much everything about the game, or just use default stuff. As a victim the idea would be to do slasher movie victimish stuff depending on the kind of character you're playing, and the setting, be it a a camp, or a neighborhood or whatever. It would kind of be like The Sims, or The Ship at first, in that you'd have your character do whatever it was that was in character for them to do while the killer stalked and watched. Eventually the character would become aware that something was wrong and then you'd have to figure out what was going on, and figure out how to stop the killer / escape and save many of the other victims as possible. If your character died or somehow escaped without the others you'd be able to switch to one of the AI controlled characters.
As the killer you'd basically have it from the other side against AI victims. You could generate/design your killer or choose a premade one with various RPGish abilities and stats, and create a theme. Then you'd be unleashed upon the unsuspecting victims. The idea again would be that you're rewarded for keeping to your theme, but also for causing the victims distress. Think Ghost Master. If you just come up behind Ashley while she's taking a walk, and then hide the body so no one can find it that would make it easier to sneak up on the others, but it wouldn't be as rewarding as say, sneaking up on her during a shower scene, freaking her out, then hiding, but then waiting until she got out the chase her naked through the woods. See?
Obviously both victims and the killer would have to be able to wield pretty much anything in the world as a weapon, and the victims could try to set up traps for the killer.