Is a mother required to fast two consecutive months because her daughter died by burning after falling into hot water while cleaning the house?

If a mother causes the death of her daughter, such as by leaving her near hot water due to negligence, then her 'Aqilah (male relatives on the father's side responsible for paying blood money) must pay the blood money (Diyah), and she must perform the expiation (Kaffarah) for killing. However, if the mother was not the cause of it, then there is no blood money or expiation upon her. Whoever kills a Muslim by mistake must perform expiation, which is fasting for two consecutive months. If the command to fast for this woman is because she caused the death and did not find a slave to free, then this is correct. But if the intention is that everyone who dies by burning should have two consecutive months of fasting performed on their behalf, then there is no evidence for this, and it is an innovation that must be denounced.