Claudia (spellsword dragonborn) doesn't carry around black soul gems around to avoid sending some one to Soul Cairn "accidentally", but she has an ongoing practical joke with them necromancers in this regard. She makes sure to take as many black soul gems as she can when going to a (psycho) necromancer's lair... They are not a fan
As for other souls.. Well so much crazy stuff happens in the grand scale in Mundus that she basically doesn't give a damn about some lesser souls.
That's also pretty much her stance on her rather cruel nature (I checked, 90 days passed the start and 900 man/mer killed by her ! ), after all they will get recycled anyway and she rather be the hunter than the hunted.
Well Mundus works on very different terms as the Heaven/Hell model. After something dies it will go to somewhere in Aetherius based on their beliefs, or Daedra Oblivion if they are servants or out of Aetherious and into Dreamsleeve to be recycled.
http://www.uesp.net/wiki/Lore:Aetherius