She wants to raise an illegitimate child with her sons
Question

                In the event that a sister dies leaving a female child, who has no other muslim relatives and father has no rights because child was born out of wedlock, although the mother of this child, became muslim.

Is it permissable for a married sister with all sons to care for the child as her own, with the approval of her husband.
Praise be to Allah.
    This child is illegitimate, i.e., the child of zina 
    (adultery/fornication), and as such comes under the rulings on foundlings 
    (laqeet), so long as his or her mother has died. It is a form of kindness to 
    this child to keep him and look after him. If the Muslim sister takes this 
    child in with her own children and brings him up, this is an act of kindness 
    and a righteous deed, but he will not be counted as one of her children or 
    one of her husband’s children, rather he will be a stranger (ajnabi), unless 
    she breastfeeds him, giving him five complete feedings, whilst he is still 
    an infant; in that case he will become a son to her through radaa’ah 
    (breastfeeding) and a son to her husband through radaa’ah. Her sons will 
    also be brothers to him through radaa’ah, but there will be no rights of 
    inheritance between them, because the relationship between them will be one 
    of having been raised together and of kindness, or of brotherhood through 
    radaa’ah, none of which bestows rights of inheritance between them and this 
    child.