Humans and demons, beasts and half-demons have a Haku and a Kon. The source of power to move one's body is the Haku, and the spiritual power to move one's mind is the Kon. In short, they are referred to as one's spirit.
Haku (魄, はく, "Soul") is the animation (or life force) of a body that is possessed by both humans and demons alike. Demons and humans that are animated by haku (or become haku puppets) do not have a soul, they are simply animated beings who are alive and are able to move. When kon and haku are unified, it is called kokoro. Haku returns to the earth when the body dies. The haku is what dictates the physical. Haku was first introduced by a demon that devoured other being's haku; Hakudōshi killed this demon, and took the haku that it had devoured. Hakudōshi used this haku to animate the bodies of different, malformed, demons that he was creating. None of these demons were sufficient, however, and each of them were easily killed by Inuyasha and Kōga's groups respectively. Hakudōshi was finally able to create a suitable and effective haku puppet, it was Mōryōmaru; Mōryōmaru had no soul or emotion, like all other haku puppets, until the Infant was placed inside of him, which gave him a soul.
After Sesshōmaru has been hit from Kirinmaru's Demon Fireball, it causes to drain his of very lifeblood essence (haku), before Sesshōmaru uses his remaining strength to send the Half-Demon Princesses, Towa, Setsuna, and Moroha into the Black Pearl as they enters to the Border of the Afterlife to protect them from further attacks. He still manages to mask his presence as his haku is gradually drained from him. Towa tried to used the Zanseiken to absorb the Kirinmaru's haku to save her father, only to end up her soul being suck and her kon have been drained leaving unconsciousness until Akuru come and revive her with his pinwheel.
According to Kirinmaru since his daughter Rion can't move anymore, her kon may have sealed within these bones and grave soil but as time passes, she will expand the haku required to move that vessel.
- Kon & Haku. The Inuyasha Companion. Harley and Dylan Acres.