How is she spending $250/week on groceries while making $9600/year? I wonder if she listed her income accurately, but maybe there is also child support or govt aid of some sort on top of that. Back when I was getting child support ( a whopping $20 a week, woohoo!), I didn't consider that income.
At 9600 / year with three kids, she qualifies for SNAP (so there's groceries), and Child Tax Credit for the three kids. She says she's unemployed but also says she's a consultant - if that 9600 a year is in unemployment benefits she does not qualify for EITC, if it's wages or some combination of wages and unemployment then she would. For a person at that income level with 3 kids the refundable portion of the tax return is going to be a significant part of their income for the year.
She likely also qualifies for housing assistance; no mention of child support but it is another possible revenue stream. And of course for some people there's always the Bank of Mom and Dad.
Even given all that, in context (and compared to other people in the same situation), $300 a month savings is great.