Doesn’t government aid nurture the desire to stay on it?

For instance, if a woman gets a set amount of State Aid per child, and if she has 6 kids, even if they are not all from the same father, and the total sum of aid for all those kids is more than she would get if she was working fast food, or some mall retail outlet, etc. Why would she go to work? If by her education, for example, she was only going to pull in minimum wage for a p/t job, and her pay would only be $650—$700 a month, thereabouts, if she missed no days, by the time taxes, rent, utilities, food, etc. is deducted she may have nothing left, or even be in the hole. She certainly won’t have any left for babysitters while she worked. But for simplicity sake, let’s say she receives monthly $500 per child, with 6 kids she would make way more sitting on her butt than she would working p/t. So, would not the government be nurturing a desire for her to stay on aid as long as possible because she can survive better than if she actually worked? In other words, what incentive would she have to go get a job when doing so would cut her monthly income by more than half?