"Erase all the Traces - Special Cleaning Service Company Dead Morning" DNF @ 41%.
A freeter (person who does various part-time jobs), 21 year-old Wataru Asai, happens to meet a man named Sasagawa at a bar after his grandma's funeral. After drinking too much Asai vomits a bit on the man's jacket and takes it to the cleaner's for him. When Asai returns the jacket a few days later to the man's office he finds an old building, and on the door to the company's office on the 2nd floor, the door simply has some tape with the company name "Dead Morning" and a cat named Castella who follows him in when the door opens.
Asai then learns that Sasagawa's little business is "Dead Morning" (Sasagawa does the cleaning and he has a secretary) and it does "special cleaning" services. That is, Sasagawa cleans the rooms/apartments where people have died either by suicide or they died alone and their bodies were discovered several days, or weeks later.