In the story of Death Note, Light Yagami becomes the ultimate mass murderer, aiming to create a crime-free world. He is joined by Misa Amane, the second Kira, and together they create their own ideal kingdom (for a time). And Light's own family paid the price.
Light's father, Soichiro Yagami, stubbornly fights for the law and justice, unknowingly becoming his beloved son's own enemy. Meanwhile, light's little sister Sayu is another victim of Light's rampage, and she represents the fall of the Yagami name in truly tragic ways. She also contrasts sharply with her scheming brother.
Sayu - The Other Yagami
Sayu Yagami appeared early in the story, and she was a typical 14-year-old at the time -- concerned with popularity, homework and TV pop idols. Like her parents, she deeply admired Light and believed in him. Sayu saw a big brother who was destined for greatness as a detective, and she spent a lot of time with him (such as studying in his room.) But unlike Light, Sayu had no inclination toward becoming Kira. Never once did she express any interest or sympathy for Kira's methods or aims and she never joined the ranks of the Kira supporters, even though she was among the people for whom Light fought. It is likely that Light considered his little sister a model "citizen" of the new world he was creating, an example of everything he was fighting for.
But Sayu felt differently, even if she rarely spoke up about it. Mainly, Sayu was frightened by the nature and power of Kira, and she wanted Kira captured ASAP. Sayu loved her brother, but she was most loyal to their father Soichiro, who was suffering more and more at Kira's hands. When Soichiro revealed that he was fighting Kira, Sayu (and her mother Sachiko) both urged Soichiro to quit the case for his own safety, but Soichiro refused. Sayu was also aware of how much time and energy Kira was draining from her father, and for that, Sayu deeply resented Kira, finding him disgusting. Finally, Soichiro himself told L and Light that Sayu is the type of person to find the Death Note, try it once, feel horror at what she did, then quit using it. This stands in stark contrast to Light, who eagerly used the notebook to control Raye Penber and kill the FBI agents in Japan, even though Light wasn't in that much danger from them. Light's innocence slipped away while Sayu's own stood like a shining beacon.
Sayu Became Collateral Damage
Later in the story, Sayu was a college student. By then, the Kira case was taking a toll on her. She did her best to hide it, though: trying to live a normal life despite the increasingly pro-Kira world that she lived in. She even thanked Matsuda, the friendly police officer, for looking out for her besieged father. Early in the story's second arc, Sayu was outwardly cheerful, thinking about ordinary matters someone of her age -- from fashion to studying. And then tragedy struck.
To get leverage on the Japanese police, Mello, the criminal mastermind, captured Sayu, daughter of deputy director Soichiro Yagami and demanded the notebook in exchange for her life. Ultimately, the trade was a success (mainly for Mello), and Sayu was returned safely to her father's arms. But the damage was done. Sayu suffered not physical but mental scars from her experience, and she was bedridden and refused to emerge from her room. Viewers only imagine what she must have been thinking and the nightmares she must have had.
Not long after that, Sayu was shown in recovery, refusing to speak and spending quiet time with her mother. Soichiro watched this scene, relieved to have Sayu back but berating himself for allowing all this to happen. He felt like he had failed as a police officer and a father, and his daughter paid the price for it. Sayu's final appearance (at least in the manga) was during a coming-of-age ceremony for young women, where she was well-dressed in a kimono and appeared happy (again not speaking). Her mental status was ambiguous; was she hiding the pain behind a smile and struggling, or had she drawn upon great inner strength to move past her trauma? Even in the best of circumstances, though, Sayu's life was shattered and her Kira brother felt zero remorse or responsibility for it.
Sayu stands for the lost innocence and happiness of the tragic Yagami family, and she helps prove that in the end, death and the notebook always win, the same role that Ryuk played. Light, and everyone he cared about, paid the price for it.