"Daddy, look! I found a kitten!"
-Dr. Burr's daughter shortly before becoming the Cheshire Cat
The Cheshire Cat is a mysterious figure in the series that can travel and communicate through electronic devices. She clearly likes Rabbit.
Role in the series
The Cheshire Cat was not always an animal. When Dr. Burr began working for The Queen, his daughter accompanied him. She would wander around the hideout, oblivious to the tragedies and darkness around her. Once The Rabbit yelled at her, which caused her to cry, initially making The Rabbit feel bad. The next day, he apologized and, for a time, they played cards together (The Rabbit would let her win), and became friends. When Dr. Burr finally succeeded in his experiments for Oystercloud, she touched the cat he was experimenting on, which caused her to fuse with the cat...becoming the Cheshire Cat.
Alice is Dead 2
The Cheshire Cat appears in a hole in the wall floating outside a vast wasteland outside Wonderland Jail. The Rabbit can peek through it, and if he looks long enough, the Cheshire Cat will approach him and flash the words OYSTERCLOUD to him, and, depending on the player's actions, may look it up on the computer database to learn about the Oystercloud project.
After the credits you can see a picture of the Cheshire Cat come into view.
Alice is Dead 3
She briefly appears on an electronic billboard in the town, signifying that she is watching out for The Rabbit. While he is in the underground laboratory, she sends him a text message telling him to find 3 tapes and watch them. When he does, he finds out the truth about Dr. Burr and herself. She activates the elevator and sends him one final message, asking him not to go up so that he won't "end up like Daddy."
It is possible that the writings in the bathroom about the "bloody eye" were a reference to the Cheshire Cat watching the rabbit.