An enemy that follows you staying roughly 2 meters behind you that will not attack unless you acknowledge his existence through either A) Running or B) looking back.
The only way to lose him would be to calmly find map out the area in your head, find an area with a door and a quick escape (with preferably more doors to close behind you) and quickly slam the door(s) behind you and run like hell so you lose him before he breaks the door(s) since he would be faster then you of course.
Imagine how scary that would be in an atmospheric game and immersive game like amnesia. You know he is
right behind you since you can hear him, you know he is stalking you like a predator and that you cant fight back, but you cant look or even run because that will just get you killed.
Of course the monster would need a distinctly unique (yet still scary) sound that lets you identify it from other monsters. scary/tense music could also start playing to let you know your in deep shit (sorta like the insanely creepy singing girl portions of this
this) just it would need to be rather quiet so you can still hear the scary sounds the monster stalking you is making.
I know i would shat bricks.
Also: has any game done this kinda thing before? I cant remember any.