Probably not, but there's the rub. How do we prevent this? Perhaps if we refuse to bail them out... but are you willing to watch a child starve to death? Will you be the one to pull the plug?
The second thing is to force mothers to reveal the father of their children. Many do not inform the state who the father is, therefore forcing the taxpayer to pay for raising the child instead of the father.
And probably the best option would be to implement policies similar to China’s one child policy. A good example would be forced sterilization after 3 children if the person receives any form government welfare (or already have kids and is imprisoned).
But in any case, well before this point, the state can spent money on voluntary sterilisation campaigns (i.e. paying the poor and drug addicts to be sterilised).
Another reason is longer life expectancy and subsidized health care. In the old days, a person inclined to irresponsible reproduction will not live that much longer than a person without. Now there are many countries with an average fertility rate well over 6.
Another reason is that it reproductive responsibility has been shown to work. Compare China to every 3rd world country (e.g. 50 African countries and India). Their one child policy not only stopped untold misery, but created the bedrock for future prosperity.