Is the mother who was looking after her infant sister legally responsible for her death, given that she was 12 years old and the death occurred because the infant left the house and froze in the cold without the mother's knowledge?

If the mother placed the child in a suitable place and took the necessary precautions, then there is no blame on her. However, if she was negligent, such as leaving the door open, then she is liable for the blood money (diyah), which her 'aqilah (agnatic kin) must pay, unless the heirs of the deceased pardon her. If the mother had reached puberty by one of the signs mentioned in Fatwa (33674), then she must offer expiation (kaffarah) by emancipating a believing slave. If she cannot find one, then she must fast for two consecutive months. If she had not reached puberty, then there is no expiation required of her.