I know there was a term or a rule for it at one point but I can't remember what it was called. Specifically at when a person expels daemonic possession by sheer force of will they are forevermore immune to chaos taint and possession. Anyone remember what that's called? And why am I remembering it as having something to do with the Illuminati?

Could the term be a "pariah"?

These are the illuminati indeed. It was old fluff, thought.

Dark Heresy 1 ed had rules for that in one of its supplements (radical's handbook, I guess)

Maybe you are thinking about the Exorcists Space Marine Chapter?

The Illumnti, that's it.

Maybe you are thinking about the Exorcists Space Marine Chapter?

No. We speak about people that, by their own will, bannished daemon out of their body and soul.

Indeed. Exorcised. There was a group in an old book (the Inquisition War Trilogy) which called themselves Illuminati, but the term for someone who's been possessed and survived the experience is an Exorcised.

It's strongly hinted that the Exorcists chapter do this to their recruits as a matter of course, and the entire chapter is therefore 'Illuminati' - whether they call themselves this or not.

There are supposedly details in Enemies Beyond for using it in DH 2nd Edition.

There is a difference between exorcized and Illuminati. An exorcized had someone else perform the exorcism to remove the daemon. An Illuminati is a human who forced the daemon out on their own.

Illuminati can freely enter the Black Library. Mere exorcized can not.