Akaneko no Akuma

Yamane Akaneko and her classmate Tsujishima meet one day in the mostly deserted second school library and discover a supernatural secret. A demon that seems like an ordinary red cat possesses Tsujishima and insists that they help him in his task to protect the books of the library. Apparently, all books that are internally consistent enough have a world that exists within them. These books are plagued by "bookworms," which look like long cats, that eat up words and change the story until its reality is destroyed. The three of them, Yamane, Tsujishima, and the possessing cat demon, journey into the worlds of many books to track down and catch the bookworms before they do too much damage!

(Source: MangaHelpers)