Board Thread:Lore Discussion/@comment-5613590-20140418110806/@comment-16047389-20140418140226

But the Chosen Undead never consumed Nito's soul, or the Witch of Izalith's. They were left in the Lordvessel. In fact, you never even acquire Seath's soul at all in the first game.

I believe that the Chosen Undead only exists in Dark Souls 2, in  that the Sublime Bone Dust "could" be their remains, as it "could" be Solaire's or any other undead that had been linking the flame for all these eons.