The child custody should take those children away.
I am saying this without judging her or looking down upon her... without malice to the doctor or the mother or ANYONE. I am not even THINKING about the welfare system.
There is no way she can take care of and afford all those kids. If she can't afford to take care of them, the children will grow up in subpar conditions, and that's not fair to ANY of them.
Part of my thinks she should at least keep two, but I think making her choose would be even worse, so all the children should be take by child custody.
And yes, it's a saddening thought, but it honestly is much better than the alternative...