Rukia Kuchiki is a highly consequential character in the Bleach story. Her first major role was to introduce hero Ichigo Kurosaki to the world of Soul Reapers -- but that's not all. Rukia is the foster sister of squad 6 Captain Byakuya Kuchiki, and her developing relationship with him had a major impact on the story during the Soul Society arc, and beyond.
Rukia knew Byakuya since before Ichigo was even born, but for much of that time, their relationship was a cold and distant one. It took Ichigo's arrival on the scene to push their relationship to its next stage, at which point Byakuya became a proper foster brother and Rukia had someone to truly look up to. It was long overdue, too, especially since Rukia had since lost her other brother, Kaien Shiba.
Byakuya & Kaien Were Two Very Different Brothers To Rukia
Rukia's original family was her much older sister Hisana, but Hisana abandoned Rukia to flee and Hisana eventually married into the Kuchiki family. Byakuya broke noble society's rules to do so, and when Hisana was on her deathbed just a few years later, she implored Byakuya to find Rukia and adopt her, which he did. Rukia, who had been living on the streets of the Rukongai district with fellow street urchins like Renji Abarai, found herself adopted formally into the Kuchiki family by her late sister's widower.
This was only a happy occasion in the sense that it took Rukia off the streets; she was now rubbing shoulders with a big brother who cared more about fulfilling his late wife's wishes more than anything. Rukia never felt that close to Byakuya, who fixated entirely on decorum and tradition, so she turned to Kaien Shiba, instead.
Kaien Shiba taught Rukia about the value of the heart -- how it's an immortal link between two people that can outlive either person. Rukia greatly looked up to Kaien as a big brother figure, more than she did to her actual foster brother. There is no clear sign that Rukia resented Byakuya or regretted joining the Kuchiki family, but then again, Rukia got very little out of Byakuya other than an example of how to be a model Soul Reaper. Only a common duty and the family name linked Rukia to Byakuya, and she meekly accepted this status quo and devoted herself to her duties. Then Ichigo entered the picture.
Byakuya Taught Rukia What Real Duty Is
During the main events of Bleach, Rukia's entire world was turned upside down -- mainly her social circle and personal connections. She was slated for execution due to Captain Aizen's scheme and she nearly lost her life until Ichigo and his squad rescued her and fought Byakuya to a stalemate. Byakuya reassessed what was really important to him as a result, realizing that personal loyalty and love trumps cold duty and tradition.
Rukia, for her part, welcomed this change, and by the time Ichigo was storming Hueco Mundo to rescue Orihime from Las Noches, Rukia and Byakuya's relationship had become what it was always meant to be: Rukia was Byakuya's pride and joy, and she proved her loyalty to her friends by going against her official orders and to Hueco Mundo to assist Ichigo. She accepted a cloak from Byakuya to protect her from Hueco Mundo's desert storms, and when she fought Aaroniero Arurruerie, the 9th Espada, she remembered the lesson that Kaien had taught her, and used the strength of her conviction to slay him.
That's not all. Soon after her rescue, Rukia found the courage to face the quietly grieving Kukaku Shiba and formally apologized for killing Kaien, who had been possessed by a Hollow of Aizen's design. Rukia had been alone for too long, and she and Byakuya both learned that opening their heart to other people was the true source of strength and purpose, not the law or duty.
Rukia repaired many of her damaged relationships at this time, making peace with the Shibas while also forgiving herself for killing Kaien and becoming Byakuya's true little sister. Rukia had a duty to all these people, and she fulfilled it just in time to face the greatest threats the world had ever seen. Rukia didn't just fight as a Soul Reaper; she fought as a loving sister who trusted and relied on her brother, and Byakuya returned the favor when he slew Zommari Rureaux for threatening Rukia's life.
Rukia's closeness to Byakuya reached its apex sometime later when she unlocked her bankai at last. Byakuya not only helped her control it, but he also praised her warmly, reducing Rukia to happy tears. Such a happy family scene was what Rukia had wanted all along.