Cheshire is a Chain that lives in a dimension created from Alice's, the Intention of the Abyss's, memories. He resembles a human form of the Cheshire Cat from Alice in Wonderland. Break mentions that Cheshire's eye was originally his own, and that the Intention stole the eye from him when she called him to give it to Cheshire.The Intention was quite close to Cheshire and regarded him as her loving cat. She normally carried Cheshire with her in the tower and pet him gently. The Intention was in great pain and cried when Cheshire was murdered by Vincent. She resurrected him as a chain because of this. Cheshire was also fond of the Intention and love her dearly, preferring her company to Alice. He wished to protect the Intention by all costs and sacrificed himself to protect Alice's memories. After Oz destroyed the Intention with his powers, Cheshire arrived at the scene. The Intention, who regain her mind and sanity, noticed Cheshire right away. Cheshire was overjoyed by this and reverse back to his original form. The Intention thanks Cheshire for always protecting her and staying by her side even when she was losing herself. The Intention told Cheshire she loved him and together, both of them was absorbed in the Rule of 100 Cycles.
The Intention of the Abyss and Alice are twin sisters, both born within the Abyss and forced to age at the same rate. The Intention was chosen over Alice to be the vessel of the Core of the Abyss, and so she remained in the Abyss while Alice was ejected from the Abyss. The Intention copied Oz the B-Rabbit by going through Alice to have access to Earth, and so she often met with the Intention at a junction in between Earth and the Abyss, where Alice would usually willingly switch places with her sister.
While it was believed that the Intention hated Alice, it is in fact quite the opposite, as she mourned Alice greatly following Alice's death, crying and screaming over Alice's subconscious self when she appeared at the junction where they often met. The Intention even told Break her wish to destroy her and save Alice. The Intention was going to have Oz destroy her memories so that Jack couldn't get to her again, as she would be unable to refuse his wishes, but when she tried this she hesitated after seeing Jack instead, Alice's soul went ahead of her sister and fused with Oz's body, allowing Alice to exist on Earth by sharing a body with Oz's soul.
Over 100 years later, the Intention once again met her sister at their junction after Oz dispelled Alice by not allowing her to remain within his body. Alice was confused by the situation at first, but in the end, the Intention returned Alice's memories to her, in order to help her understand why things had to be the way they ended up. After learning about Break's encounter with her sister, Alice was determined to save her sister. She came to the Intention of the Abyss's rescue after the Core swallowed her. Alice showed the Intention of the Abyss her memories to help her sister understand what was happening. The Intention, overjoyed with being together with Alice and seeing Jack again, was grateful.
100 years ago, Alice, the Intention of the Abyss, met Oz when she was born and seems fond of him, saying to Jack that this rabbit was always there by her side. Unfortunately, the Core gives Oz the piece of Lacie to deliver to Jack, and thus causes one of his bodies to die.
However, she seems to not have paid as much attention to him as her sister did, given that she forgets Oz's name constantly, preferring to call him B-Rabbit instead.The first time they met (when both Oz and the Intention had lost their respective memories), the Intention of the Abyss thought that Oz was Jack. She seems to think of him as a reincarnation of Jack Vessalius and is thus deeply infatuated with him, and shows jealousy at Oz choosing Alice over her, stating he would "regret it." Oz himself stated that he
It is confirmed that Lacie was the mother of the Alice, Intention of the Abyss, and her twin sister Alice. They have never met before, but the Intention of the Abyss and Lacie shared similar traits such as dancing in blood and having damaged personalities and constant mood swings. Just as Lacie had an interest in Jack, the Intention of the Abyss also held the same interest. She also seems to know more of her mother than Alice does and remembered the song Lacie used to sing, 100 years after she lost her memories.
Levi was the confirmed father of the Intention of the Abyss and her twin sister Alice. They didn't seem to get along too well and he apparently never told her she was his daughter.