A mutated cat enemy was planned for the game but ultimately not included. However, a stuffed version of it can still be found in the underground base of the "Duty" faction.
Poltergeists are invisible and can telekinetically throw objects at the player, though they're mutants rather than supernatural creatures. A variant called Pyrogeist is similarly invisible but conjure gouts of flames to attack.
There's a relatively infrequent type of enemy called a "controller", which attacks you by freezing you in place, and a camera zoom is triggered. So it's kind of implied to be trying to mess with your mind, but it's not really possession.