Chloe didn't know from where that feeling came. She wasn't Claire's mother, nor sibling, or anything like that. She was just an acquaintance, someone that knew her under harsh circumstances and had empathy with her.
However, no matter how much she tried not to create bonds with that girl, she always ended up loving her a little more every day. In the start, the only thing she did was to give her company and talk to her frequently, so she would be able to calm her down. Claire had panic and anxiety attacks from time to time that didn't let any of the other girls sleep, thus she needed someone to stay with her during those harsh days.
However, from a little bit of comfort and talking, her actions grew to something way greater and meaningful for both of them. She began to get bolder when it came to protecting Claire. She covered her in the Red Room, making her suffer the least possible. She even defied their superiors and deceived them, so they wouldn't do anything to her.