「Chocolate Puma」
The four Stands become "anchor points", acting as the corners of their area of influence. Living things insde this area of influence will have their souls separated from their physical bodies. Stand users can still use their Stands, but at a somewhat weakened state (they perform at roughly 70% efficiency). Their souls become invisible to living creatures, but their Stands can still affect the world. Because of this, their unconscious bodies are vulnerable. The Stand user can choose who to trigger this effect on. The effect ends when all four Stands are defeated or the user recalls the Stand. The Stand has a cooldown period after it is recalled or defeated.
The four Stands must be found and defeated to lift the effect. There is a time limit (maybe an hour) or the victims will die. The maximum area of effect is roughly a mile, the Stands can defend themselves somewhat, but will tend to hide as their movement range is limited while they're using this ability. When a Stand is defeated, its "corpse" will still act as an anchor point until the effect is lifted.