Not necessarily.
Let's say we just passed legislation which said that
(A) if a current recipient of means-tested assistance has an additional child, that the benefits level would not be increased as a result, and
(B) Medicaid would provide free long-term birth control (IUD, Norplant, etc) and free sterilization to any Medicaid recipient.
Changing the rules so that there is no benefit to be gained by having a child on welfare IS NOT the same as making people die on the streets.
It is when they go ahead and have the children anyway.
What is left out of your equations is the fact that people in the underclass, to a considerable extent by definition, do not organize their present activities around long-term perspectives. As is shown by their lifestyle.
So while such a policy would reduce births to unmarried and perhaps unemployable mothers to some extent, it might not reduce it all that much. And when a mother of five isn’t able to feed her children, we’re back to starving in the streets.