Death Of A Demon?

Inconsistently, mythologies describe at least two kinds of death, e.g.:

a warrior dies in battle but his spirit goes to Valhalla;

in Valhalla, the spirit functions exactly like a body because it feasts, fights and dies but then is resurrected to feast and fight again;

however, when it eventually dies at the Ragnarok, there will be neither a surviving spirit nor a new resurrection.

In Christian theology, there are several kinds of immortal spirits:

God;
angels;
demons (fallen angels);
human souls.

However, in works of fantasy, the status of demons becomes a bit more complicated. In Poul Anderson's Operation Chaos (New York, 1995), Steve Matuchek, werewolf, bites the throat of a succubus. The "...foul spirit within..." (p. 118) the succubus tries to flee to the Low Continuum where it will change places with "...the exchange mass." (ibid.) However:

"The body perished and the soulless demon was no more." (ibid.)

Usually, we understand that a demon does not have a soul because, like a soul, it is a spirit - but such a spirit should survive the death of any body that it has possessed or inhabited?

In Lucifer: A Dalliance With The Damned (New York, 2002) by Mike Carey, Lucifer tells another demon:

"Most of the options I'm considering run into the same problem. That you have no immortal part. Destroying you outright would scratch an itch, but it wouldn't make the point.
"So at great trouble and expense, and at the risk of creating a very awkward precedent --
"-- I'm furnishing you with a soul." (p. 133)

A demon has no immortal part and can be destroyed outright but can also be furnished with a soul? Fantasy writers, like sf writers, are not supposed to make up the rules as they go along...

However, authors like Anderson and Carey write so well that they usually carry it off. Their narratives seem to be and indeed are deeply meaningful even if they still raise some questions in the mind of the inquiring reader.