Prior to the events of the game, Futaba was the daughter of esteemed researcher Wakaba Isshiki, a leader in the field of "cognitive psience". At an early age, she showed signs of genius-level intellect. In elementary school, she attempted to showoff her skill by claiming she could memorize an entire bookshelf of titles with one glance. When the other students saw her do just that, they ostracized and bullied her.
However, one student, Kana, found her skill impressive, and the two became fast friends. That friendship came to an abrupt end when, by accident, Futaba saw the inside of Kana's diary and memorized its contents. Kana immediately deserted Futaba, leaving her friendless until she meets the Phantom Thieves. During her Confidant arc, she becomes visibly depressed when she recalls her elementary school years.
Futaba had a strained relationship with her mother. Constantly busy, Wakaba was unable to take much time off for Futaba, and Futaba began to resent how little attention she was paid in comparison to Wakaba's research. While in the process of finishing up her thesis, Wakaba unexpectedly commits suicide, an event Futaba witnesses first hand. Futaba begins to blame herself for Wakaba's death, in part due to a forged suicide note that chastised her as a hassle that only held her back. Likewise, her surviving family resents her, and she is passed around from guardian to guardian.
Her uncle, in particular, subjects her to physical and psychological abuse. Locked in a room with no bed or any means to clean herself, Futaba begins to develop clinical depression and, later, schizophrenia. She is eventually rescued by Sojiro Sakura, a former associate of Wakaba, who later adopts her.
Although safe from harm, it becomes clear that Futaba was permanently scarred by the events of her mother's death. Sojiro attempts to rehabilitate her, even consulted numerous psychiatrists, but Futaba's state only deteriorates, until she ultimately refuses to leave her room. It is likely around this time that Futaba starts to hone her skills as a computer hacker, for the purposes of understanding her mother's work, and the circumstances surrounding her death. She also moonlights as a cybercriminal named Medjed, which later became a network of "hacktivists" that used her toolset. After the group mutates into a cyberterrorism front, Futaba adopts the handle "Alibaba".
In Persona 5
Futaba is able to bug Sojiro's place of business, and therefore spy on the Phantom Thieves. When the Phantom Thieves are accosted by Medjed into revealing their identities, Futaba intercepts Joker's phone and negotiates a deal with the Thieves: "steal" the heart of Futaba Sakura, and she will protect them from Medjed. The team reluctantly obliges, unaware that Alibaba and Futaba are the same person.
Noticing how their target bares the same surname as Joker's caretaker, the Thieves begin to suspect that the two are related. Futaba's existence is kept hidden to most people in town. When Joker is tipped that Sojiro has been accused of abusing his daughter in secret, he presses Sojiro to confirm he has a child, which he initially denies. Undeterred, the Thieves sneak into the Sakura resident, and confirm that a young girl is living there. When they are caught by Sojiro, he reveals Futaba's troubled past, and why he elected to adopt her.
The Thieves return to the Sakura residence, hoping to speak with Futaba in-person and gain entry into her palace. While she refuses to even open the door, let alone speak to them, she talks over text message with Joker and Makoto Niijima. Futaba states that she wants to die, and that she considers her room to be a tomb.
The Thieves are given enough clues to enter her palace: a pyramid amidst a barren dessert. Unlike the other palace guardians, Futaba's shadow is not outright antagonistic towards the Thieves. Upon arriving at a locked door, the Thieves elect to speak to Futaba face-to-face, to remove any emotional barrier between them. With considerable reluctance, she unlocks her door, and the Thieves present her with a calling card.
The Thieves face off against a false manifestation of Wakaba, whom Futaba has conjured up after years of self-loathing. Futaba, meanwhile, discovers the Navigator app on her phone, and is able to enter how own palace, where she encounters her shadow. Futaba's shadow confronts her, and challenges her to consider if Wakaba had been murdered. Realizing that her mother cared too much for her to have written such hateful words in a suicide note, she rejects the idea that Wakaba hated her, triggering her awakening. Unlike the other Phantom Thieves, she inherits her Persona through a shadow transformation, akin to the cast of Persona 4.
With Futaba's navigation aid, the Thieves are able to eradicate shadow Wakaba, erasing the poisonous through from Futaba's psyche. Futaba then falls into a light coma, but awakens in time to hack into Medjed's homepage and threaten them into submission.