Spoilers................................................................................................................................................................................................
I think Coco was dying due to something about Kuro's nature (I don't think he would purposely hurt her).
After she remembered the accident and saw her parents' dolls, she realized the people were right and that Kuro was a monster...but he was still her friend, so she offered for them to merge.
He did so. This brought her hair back to being black and made Kuro disappear, so everyone else thought she had gone back to normal...but she really had gone to being half-Kuro. Since Kuro was a part of her now, she could see him (and other monsters), and she would see him even when he was part of her. Everyone else thought she was better and thought she needed a new cat, so they got her one.
I'm a bit confused towards the ending. Does it mean this whole time, Coco was in a coma and end up dreaming the whole thing. And Kuro helped her getting out of that sleep by parasitize inside her?