Barbara

From the Digital Manga edition

Wandering the packed tunnels of Shinjuku Station, famous author Yosuke Mikura makes a strange discovery: a seemingly homeless drunk woman who can quote French poetry. Her name is Barbara. He takes her home for a bath and a drink, and before long Barbara has made herself into Mikura's shadow, saving him from egotistical delusions and jealous enemies. But just as Mikura is no saint, Barbara is no benevolent guardian angel, and Mikura grows obsessed with discovering her secrets, tangling with thugs, sadists, magical curses, and mythical beings - all the while wondering whether he, himself, is still sane?

Source: Anime News Network Encyclopedia