I am watching Elfen Lied for the first time. I am about 3-4 minutes into the first episode, so if I happen to create something that is later revealed in the series I am not ripping it off.
The naked girl in the iron mask just backed the lone living guard into a corner and killed him off-camera. His blood ran down the edge of the wall. Then, a bloody handprint with no accompanying limb smeared against the wall and wrapped around a lever to open a door.
My quick idea: A form of possession where the spirit does not inhabit and animate the body but, rather, accompanies it. So, the invisible spirit floats along beside the possessed creature, whispering in its ear and doing its* bidding (perhaps based on telepathy, perhaps based on a combination of observation and great wisdom in reading people).
*This "its" can refer to both the possessed creature and the possessing spirit, depending on the temperment of the spirit. For example, a creature so possessed might find that the spirit does whatever the spirit wants, killing friends and loved ones and allowing all the blame to fall on its haunted host. On the opposite end of the spectrum, the spirit may do whatever the host wants, acting as the host's hands and feet. In such a case, what the host offers the spirit would need to be determined (feeding on his soul; trying to corrupt him by offering the great power the spirit possesses; etc).