The Blanket Cats by Kiyoshi Shigematsu

In Tokyo, there is a shop where you can rent a cat for three days. The cats are many different breeds-Manx, Maine Coon, Calico, American Shorthair, and Russian Blue. They also come with a blanket which needs to be with them when they sleep. The Blanket Cats tells the stories of seven people who take a cat home, like Taeko, who's on the run after taking a lot of money from the company she works for. One story is from the point of view of a cat named Tabby, who escapes from the woman who rented her and goes on to protect two children who have run away from home. A great read-alike for The Curious Kitten at the Chibineko Kitchen and the Kamogawa Food Detective series.