Kotone is a close friend and classmate of Rin Tohsaka. Rin stands up for her in class when she is bullied and work is forced upon her by the librarian.
Kotone respects Rin, and Rin is proud of the trust Kotone has for her.
Kotone is one of the many children kidnapped by Ryuunosuke Uryuu and Caster for use in their various human projects and sacrifices. After Kotone disappears from school, Rin realizes the disappearances are related to Holy Grail War in some way, and feels that she is the only one able to help her. Rin ventures into the city to search for her alone.
In the original novels, it is implied that Kotone meets the same gruesome fate as most of Ryuunosuke and Caster's other victims during the novel. Rin begins to despair that the hope of finding her alive is slim, and eventually even thinks that she should have aimed to find her remains in the first place. She is never referenced again afterward, and she is said to have a "murky fate."
The anime version of the events play out differently, as Rin manages to follow Ryuunosuke to an old building where he is keeping a number of children. She finds Kotone among them, and she manages to save them all by shattering the magecraft that was holding them in a trance. Kotone returns to school afterward with the other victims.
« In the first draft, I unthinkingly named her "Satsuki" and ended up getting punished by the original author. I had totally forgotten that Satsuki was Sacchin's real name – or rather, I had forgotten that Sacchin even had a real name at all! To all the Yumizuka Satsuki fans around the world, I humbly beg your forgiveness.
 Fate/Zero material - Encyclopedia: Kotone [Person's name], p.095-096
Kotone [Person's name]
Rin’s classmate, who was kidnapped by Gilles and Uryuu, umm…a girl with a muddled fate.
During the first draft, the name “Satsuki” was picked without thinking, the author forgot about Sacchin’s real name up until the original author’s punishment – he even forgot the fact that Sacchin had a real name.
Yumizuka Satsuki fans all over the world, we must respectfully apologize.
Kinoko: “Fujibuchi, be a little more considerate…”
Gen: “If she (the target of the teasing) is not called Satsuki, she’s not moe.”
Somehow this conversation happened but didn’t happen.