So, we know that she used to be some celestial entity, who was in charge of Judging the Dead (I think there is a direct quote, but there is also a bit about stone faced court and spiders in the well). Then, there is a small quest about something called "the watcher" going silent in the White Well.
So it seems like Eccentric used to be "The Watcher", however I am not entirely sure. Had anyone deposed the cat at the White Well, by any chance? Maybe there are more lore about this whole deal.