The father is responsible.
If you can’t do the time, don’t do the crime.
Ultimately the women decides whether or not to have a child. Therefore the woman is responsible. If a women cannot see to supporting her child either by working or having a supportive father of the child then she should not have a child. If she has child she cannot support than adoption or an orphanage are good options if family or church will not step up.
The last thing that should happen is that society should be forced to support her and the child or even forced to help her force the baby daddy into supporting the child.