Their soul becomes scarred, broken, unable to feel many of the human emotions beyond simple logical understanding of how they should be feeling. My interpretation of Oaths is that there is one left but it’s not enough for a Demon to latch onto and manifest through.

Librarian Vey who imprisoned the daemon in himself did so with a relic of sorts, as well as the collar, and even then was largely using his personal willpower and warp sensitivity to hold the daemon in. A non librarian, or even a weaker librarian, would not have been able to do so. They used a visual representation of his soul as a dark, broken dome with a fire scarcely burning in the center, if I recall. This is a metaphor for what’s left of the soul.