Sayu's father was the owner of well-known frozen goods company. However, his father was a frivolous man that commit adultery left and right. Right before Sayu's born, Sayu's dad cheated again, and force Sayu's mother to aborted her. However, she refused and deliver her. This makes her father left, and slowly turn her own mother to hate her. Her older brother was quite talented and named as her father successor. Although her brother was quite distant, he cares for Sayu.
At high school, she was aloof to her surrounding It changes when one of her senior confessed to her. She rejected his confession, but one of Sayu's classmates has crush on him, and fault Sayu for it. Sayu remained aloof, and another of her classmates (Yuuko) asked her to be friends, because she was attracted to her indifferent attitude. It took turn to worst, when the bullying turned to her, eventually drove Yuuko to suicide. Sayu took a break from school for a while, and her mother confronted her, more concerned from publicity of the case and their family standing. Then she started to accuse Sayu was actually killing Yuuko. This make Sayu snapped and ran from home. Her brother intervene, give Sayu 300,000 Yen, and ask her to cool off for a month elsewhere. He gives Sayu a cellphone, and ask her to call if the funds ran out or if she encounter any trouble. The money eventually gone, but Sayu still won't contact her brother. Although her brother love her, she can 't stand to be forced to live in that house again. She started to offer herself on the street, and live on as runaway since.
If you want to know what it's like, read: https://mangadex.org/title/31848/blue-hearts Chapter 21-29.