Chambara Villain/Hero Catwoman.
Growing up on the mean streets of Osaka, Shina Kiryū fell in with a crew of assassins and bandits under the tutelage of an exiled ninja. She was one of his greatest students-- and later made a name for herself independently as the master thief and kunoichi, Bakeneko.
Shina lives in a ramshackle temple on the edge of town. The dilapidated structure has been empty of humans for years, and now houses a hundred or so feral cats. Shina feeds and takes care of them, thinking of them as her family.
Shina's relationship with the Kōmori Yasha is complicated, as they both live much of their lives in the shadows, outside the rules that govern normal society. She has made her feelings plain, but his all-consuming mission too often interferes.
(A note on translation: I went with "ghost" instead of the more common "monster" because it fits the idea of a thief better. Neither is the literal translation of "bake", meaning "changing or disguising", so I feel justified.)