I think one big takeaway from this conversation is that because the federal gov't is the federal gov't, the date on unemployment statements representing the end of a person's federal "benefits' (I hate that word in this context) will more often than not show that there is remaining eligibility even when there isn't because the program ends on September 4th.
Also, if an employer wants to report that someone who is on unemployment has refused a job offer, the direct link to the necessary form is here: https://docs.google.com/forms/d/e/1FAIpQLSfDqhB-bSE670mSBOv_vQQQMrN3r3jrgQQ8ME9bbvoZzhYv1g/viewform
Photo: Intern, Temp