The existence that governs the Abyss. Usually appears in the form of a bloodied rabbit doll with big round eyes. The real form of the Intention of the Abyss is Alice with white hair and clothing. It was thought that the Intention of the Abyss wanted Oz and Alice to go back in the Abyss. The Intention of the Abyss and Alice are somehow connected. She also has powers such as destroying Chains, switching between the Abyss and the outside world and changing the Past.

Spoiler

The Intention of the Abyss and Alice Baskerville are twins who were conceived in the human world and born in the Abyss at the same time. Both are truly named Alice but Revis (Glen) called her "The Will of the Abyss" as part of his experiment. After Lacie gave birth to her, she touched the core of the abyss and became its vessel. The Core is able to take over of her body whenever it wants. The Will is also able to switch places with her sister whether by asking or forcing her. She gave Lacie's fragment, after being cast into the Abyss, to her stuffed rabbit Oz so Jack could receive it. After her birth the Abyss started to lose it's light and that would come to reside within her, she also lot the ability to smile. It was later on revealed that the Intention of the Abyss made Xerxes Break promise her that he would set her free from being the Intention of the Abyss and to save Alice. She was the one who created B-Rabbit after being asked by Jack. She was fond of him and decided to help him fullfil his wish, which was to destroy the chains that surrounded the world. Up to the chapter 72 it's possible to notice that she was the good Alice, the one that was always playing with Cheshire and chatting with Jack. White Alice decided to destroy her memories in order to stop her from helping Jack after finally learning about his real intentions. Before Black Alice could help her wipe always her memories, the Core of the Abyss took over and stopped this from happening, thus scattering part of White Alice's memories and mixing with her sister's.

Her name given by the fandom is Alyss to differentiate her from Alice. (Source: Wikipedia)