I've posted this here, since it's more general Lore than anything else.

In the games, obviously, you cannot steal a Soul Trap and the Soul Trap automatically knows who cast it; but is there anything in the wider-Lore about how Soul Trap spells actually work, and if there's a way to intercept them? Like, what happens to the Soul if you have no Soul Gems? In-game, you just lose it, but would it be possible for someone else to claim that Soul instead?

I seem to recall something about a machine which used Souls as a power-source, or something, but it was only something I read about in passing, so might be totally different; but then we also have Azura's star, which is a special Soul Gem, anyway, so could it maybe 'take precedence' over other Soul Gems in the area?

http://www.uesp.net/wiki/Books:Ingenium#Ingenium from the two novels. It didn't as much use the souls as it shunted them into Clavicus Vile's realm in exchange for him keeping the Ministry of Truth aloft. The Ingenium was later rebuilt as the core of the reincarnation cycle on Umbriel.