Children will suffer either way. You can accept a relatively small amount of suffering and address the issue in the here and now (stigmatize the women, pose alternatives like adoption, thus set an example of what not to do) or you can go the other route (make excuses, subsidize their behavior) and end up with a massive self-perpetuating culture of single motherhood, dysfunction, and criminality in the long run. We're currently seeing the latter. If you thought eugenics was terrible, consider what the opposite would look like.
Those are just two ends of a spectrum. There are plenty of ways to address this. Personally, I'd immediately end the drug war (thus massively alleviating single-motherhood in black communities) and look into changes to divorce/alimony law and the family court system. Ending the aforementioned subsidies referenced by the OP would be massively beneficial as well. Unfortunately there are a lot of entrenched interests associated with everything I've just mentioned, so barring some sort of catastrophe, I suspect a cultural/social approach (e.g. stigmatization) is likely to be the most immediate and realistic place to start.
Without welfare, the mother would likely give he children up for adoption by responsible people that can afford them. At least she would have that choice, and the choice to raise the children in poverty, thus causing them to suffer, would still be hers.
Judging by the responses to my "boilerplate," inluding yours which consisted of a run of the mill ad hominem attempt to shut down the conversation by white knighting, and others which were non-arguments and sarcastic these are not arguments that people have considered.
Then children will suffer.