Moon Edge(2010)

Moon Edge

In a ruined city, Takeru comes across a suicidal young girl named Konoha. She's deathless, and she's being used as a guinea pig by a cruel organization. Seeing no meaning to her life, she fled her captors to seek a way to end it. Takeru has a lot in common with Konoha-- he's also deathless. He's made a life for himself, though, locating people by contract. After he rescues her from her pursuers, he convinces her to continue living. Maybe she'll be able to find a purpose, as she and Takeru face the future together.

(Source: MangaHelpers)