If someone employed from the US government somehow gets on unemployment and they continue to make their claims of being unemployed, they can just illegally keep their claims going, because no one from the US government is going to tell them they were rehired and getting paid. They can commit fraud easily. Of course, they will likely be found out eventually.
I doubt that the systems even talk to each other. Of course Virginia was pretty f-ed up when I lived there. Of course, I never lived there long enough to pay any income tax to the state.