The Secret Sakura Shares — Akira Hagio

When Aoi Narinomiya, the last daughter of a prestigious family, discovers that her grandfather has gone missing, leaving her to carry an astronomical debt, both she and her dog, Sakura, are inches away from finding themselves on the street. When her enigmatic classmate Kei Katsuragi shows up on her doorstep to repossess everything her family once owned, Aoi makes a desperate plea for Kei to take in her beloved Sakura--maybe she could at least be spared...?
It seems, though, that Kei is far less interested in owning a dog than he is in calling a pedigreed kitty his own, and Aoi soon finds herself playing the part of the young man's prized pet! Disturbingly, it turns out to be a comfortable and reassuring life that Aoi feels she hastoo quickly settled into, but could Kei have ulterior motives that go beyond just "owning" her?