What's the Name of That Book??? discussion

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Cut Me Free
SOLVED: Children's/YA
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SOLVED. YA: Girl without name is physically abused by father regularly, lives in attic with little brother. [s]
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PLOT (from the odd details I remember):
An unnamed girl (12-15?) and boy (8-10?) live with their abusive parents. The father regularly abuses them using knives/weapons from a closet of weapons he keeps. He cuts their backs and burns them at least once a week. While one kid heals from the abuse, the other is abused; they take turns being cut up by their sadistic father. The mother only watches the abuse and never gets involved.
The boy and girl give each other names because their parents decided that they do not deserve to be named (I do not remember any names). The children's grandmother discovers the abuse but is silenced (not sure how) by the father. The children attended school briefly, but were removed from it because the parents thought they might be discovered as abusers.
SPOILERS
The boy eventually dies from the abuse and the girl is forced to bury him. She takes the opportunity to escape, hitting her father over the head with a shovel, believing she killed him, and runs away. She runs away to a large city (maybe New York?).
She needs a fake ID (can't remember exactly why but I think it is because she needs ID to work/earn money). She meets with a teenage boy to get the fake ID and he is romantically interested in her, but the girl is afraid of being abused again.
She sees a young girl in the park being roughly tugged along by a man. The man presses on one of her bruises as they walk to keep her from getting help from strangers. The protagonist recognizes the signs of abuse and follows the girl and man back to his apartment, hoping to save someone from experiencing the abuse she did. She eventually breaks into his apartment and rescues the girl. During the fight, the man's apartment is lit on fire. Not sure of this-- but the man somehow knows her father and her father comes back in the end?
I've been looking for this book for years! Any ideas would be greatly appreciated.