She covered her child with a thick blanket and he died

If she had covered his face with the thick blanket, then she
has to offer expiation for accidental killing, and the diyah must be paid by
her ‘aaqilah (male relatives on the father’s side), because it seems that he
died because of that. If she did not cover his face, then she does not have
to do anything and no one has to pay the diyah. 

In the answer to question no. (52809),
we have explained that in the case of accidental killing, the diyah is to be
paid by the ‘aaqilah of the killer, and not by the killer himself. In that
question we have also explained who the ‘aaqilah are. 

Ibn Hazm (may Allaah have mercy on him) said in al-Muhalla
(11/15): Concerning a woman who slept beside her son etc and he was found
dead. Then he narrated that Ibraaheem al-Nakha’i said concerning a woman who
covered her son’s face and he died in his sleep: She has to free a slave. 

Ibn Hazm said: If he died because of her action, such as if
she put the blanket over his face then he fell asleep and suffocated and
died, or her arm fell over his mouth, or her breast fell over his mouth, or
she rolled on top of him without realizing, then undoubtedly she has killed
him by mistake and she has to offer expiation, and the diyah must be paid by
her ‘aaqilah or by the bayt al-maal. If he did not die because of her
actions, then she does not have to do anything and no diyah has to be paid
at all. 

If she is uncertain as to whether he died because of her
action or not, then no diyah or expiation is required in that case, because
we are certain that she is innocent of killing him but we are uncertain as
to whether he died because of her actions or not. Wealth (of others) is
haraam unless there is certainty, and expiation is an obligation of
sharee’ah, and nothing is obligatory in sharee’ah unless there is a text or
scholarly consensus. It is not permissible to impose a penalty or fasting,
or to oblige her ‘aaqilah to pay the diyah, on the basis of false
speculation. And Allaah is the Source of strength. End quote. 

It says in Fataawa al-Lajnah al-Daa’imah (21/373)
concerning a woman who covered her nursing infant with a heavy blanket when
he was sick, and he died: If the blanket which with his mother covered him
was covering his face, then she has to offer expiation for accidental
killing, because it seems that he died because of that. This expiation is to
free a believing slave; if she cannot do that then she has to fast for two
consecutive months or sixty days. If she is sick then she may fast after she
recovers from that sickness. End quote. 

It also says (21/387): If your wife placed the blanket over
the child’s face and that resulted in his death by suffocation, then she has
to offer expiation… but if she did not place the blanket over his face, then
she does not have to do anything, because she did not cause his death. End
quote. 

It also says (21/388): If you did not put the bedsheet and
quilt, or one of them, over her face, and they fell over her face because of
her movements, then there is no sin on you because you were not careless.
But if you put the bedsheet or the quilt over her face, then both of you
must offer expiation for accidental killing, because by doing that you
caused her death. End quote. 

And Allaah knows best.