He Won't Kill, She Won't Die (Korosanai Kare to Shinanai Kanojo)

Following the comic book of the same name high school student Rei bears no interests and is listless. he is boring and bored. Rei sees his class-mate Nana bury a dead bee with care and respect. Rei becomes interested in Nana and even more so after she confides in him that she has no will to live and is harming herself.