Shinigami Rock

Myoga, a timid man who is used to being taken advantage of, is in charge of managing souls in the afterlife. He is given the task of managing the "M" ward, a place where evil souls are housed. There, he meets Satsuki, a messed-up criminal, but she feels strangely comfortable with him? "Show me that you're not boring."

(Source: Shounen Hana to Yume, translated)