Arkanis Gauth is the thief that appears and kills you if you go on a killing spree in the thiefs guild if you didn't side with Bodhi. He's put in the game to stop you ruining the story line if you try and kill the thiefs and sided with them. He is invincible apart from sucking his brains out that's the only way to kill him as Dundee mentioned.
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He also helps you fight the vampires in chapter six if you ask for the Shadow Theives help. He isn't invincible this time though.

Dundee I've never killed Arkanis Gauth before I tried but he killed me.