Sof davar, there are MANY children who come into this world and have no father, i.e. he died in the army or in an accident, became ill and died, or the parents divorced. While it may not be an ideal situation, if the mother has a close supportive network, her children will never lack for love.
As to stigma – only mean spirited people would stigmatize such a child. This is not the Dark Ages. Not everyone can or wants to adopt. If a woman has a biological urge to reproduce if possible, who are we to deny her that? yes, there are kids who need foster homes, but that is not up to us to decide for someone else.