Typically drs release you to go "back to work" after a c-section at your 8 week checkup. Vaginal is 6 weeks. So, she will probably not be able to collect for that at least that 8 weeks of time.
They also may ask her to verify that she has acceptable childcare so that she is considered "employable". As other mamas said below unemployment insurance is to be collected while you are actively seeking employment and looking to start back to work, not to stay home and raise a child. If she is collecting without looking and/or being prepared to work she is committing fraud and could face re-payment of all benefits as well as fines. If she is audited she will have to PROVE that she was applying to jobs (usually between 2-5 PER WEEK, depending on the state).
It sounds harsh, but it seems like she is taking advantage of unemployment. What was her plan for income when she was employed part-time with no paid maternity? That should be her same plan.
She may qualify for WIC or foodstamps since she will have no income. It depends on the household income so if she's married or living with someone that will factor in.
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ETA: I just saw you're Chicago. IL doesn't have state disability for maternity. She can apply for the link card and maybe emergency child care. Also they have "kidcare" and familycare insurance that in some cases can be retroactive 3 months.