By all means this woman should receive government assistance.

The government should assist her in relocating these kids to the homes of unfortunate, caring couples who cannot have children of their own... but are perfectly capable of raising some. It's a "win-win-win" situation. The kids win by getting a fair shake in life, being raised with the proper love and attention. The new parents win by getting their lifelong wish of having children to raise and care for. And the "shit-for-brains" hamster...er... woman wins by getting a huge load and responsibility off her back. One that she can ill afford to perform correctly.