Frame Saber (フレームセイバー) is a manga written and illustrated by Tomomasa Takuma. It was serialized in Comic Gum.
The "saber" are immaterial entities that take possession of the body housing to protect our world by exterminating the "frame users" from another dimension. So that when possessed the bodies hosting lose consciousness, Kaon, our heroine, keeps hers. How would she cope with horrific monsters who threaten it now?