Kairi is a main character who as in the game, lived on Destiny Island. During the time she is on the Island in episode 2, Sora and Riku call her Kaina, Yuri and Yuna. They seem to be intent of ditching her as they run away from her in episode 2 and then talk about how find her Homeworld and then leave her there. In Episode 10, Riku has another flashback where they plan to leave her in the cave until there voices break, but just after that there voices do break so they have to think of a new plan.
When Darkside destroyed the Island she was taken to Malificent where she was apparently tortured. Malificent attempted to kill her but she sat up and started giggling.