Katsuki is a boy Misae Sagara met many years ago. She encourages Shima to recover when he is still in his wheelchair. Their meeting leads to the event in Misae's path.

Spoiler

It turns out that he is a cat kept by the real Shima, who asked the cat to grant Misae a wish before dying.

Several years ago when he was still in a wheelchair he met Misae in a hospital and was encouraged by her to recover. Eventually he finds her again and wants to thank her by granting her wish.