I didn't read the article , as I feel I don't have to to comment, as I have strong feelings in this regard and have read many stories of the like.
Welfare is a hand up not a hand out and a way of life. If her multiple husbands are not going to be fathers and provide , the best thing for the children is to cut off all subsistence. Have child welfare move in and remove the children. either place them in foster care, or orphanage for adoption where they will receive proper care , proper schooling , and hopefully break the welfare cycle and give them an opportunity for a better life and a better chance to succeed and become positive contributors to society.
JMHO