She covered her daughter with a light cover when it was very cold and the girl died
Question

                Thirty-seven years ago my mother had a baby girl, who was sickly from birth and could only breastfeed with difficulty. She lived for two months like that, and it was winter time. Every night my mother covered her with two blankets because it was very cold, but on the last night the cover was simple (i.e., just one blanket). In the morning she found the baby girl in a bad way, then she died after that. 

She does not know whether she caused her death; does she have to offer expiation of fasting for two consecutive months, or what should she do?

Please advise us, may Allah reward you with good.
Praise be to Allah.
      The basic principle is that she is innocent unless it is 
      proven that the offence was committed and that she was the cause. If it is 
      proven that the girl died because of severe cold, then your mother has to 
      pay the diyah and offer expiation, because of her negligence and causing 
      the death of her daughter, unless the heirs of the girl agree to forego 
      the diyah, in which case it is waived. In the answer to question no.
      52809 it is explained that 
      the diyah in the case of accidental killing has to be paid by the ‘aaqilah 
      of the killer (male relatives on the father's side) and not by the killer 
      himself (or herself); in the question referred to there is also a 
      discussion of what is meant by the ‘aaqilah. 

    If it is not proven that the girl died because of the severe 
    cold, or there is some doubt concerning that and it is not certain, then 
    your mother does not have to do anything, because the basic principle is 
    that she is innocent and an offence cannot be proven on the basis of 
    suspicion. 

    Ibn Hazm (may Allah have mercy on him) said: If he [the 
    infant] died because of her [the mother’s] action, such as if she put a 
    blanket over his face, then he slept and turned over and died of 
    suffocation, or her arm fell over his mouth or her breast fell on his mouth, 
    or she rolled on top of him without realising, there is no doubt that she 
    killed him by mistake, so she has to offer expiation and the diyah has to be 
    paid by her ‘aaqilah or by the bayt al-maal. If he did not die as a result 
    of her action, then she does not have to do anything or pay any diyah at 
    all. 

    If she is not sure whether he died as a result of her action 
    or otherwise, then no diyah is to be paid in that case and no expiation is 
    to be offered, because we are certain that she is innocent of killing him, 
    but we are not certain whether he died as a result of her action or not, and 
    wealth cannot be taken except on the basis of certainty. 

    The expiation is a shar‘i obligation, and shar‘i obligations 
    cannot be proven except with a text or scholarly consensus. It is not 
    permissible to impose a penalty or a fast, or to oblige her ‘aaqilah to pay 
    the diyah on the basis of a false suspicion. And Allah is the source of 
    strength. 

    End quote from al-Muhalla, 11/15.