International students can actually work up to 20 hours per week while studying, but that still just lets you cover some expenses at a student wage.
It is against the law to overstay your visa. No one is likely to come and chase you down, but there is a chance of getting caught and expelled if you are entangled with the law for some other reason (perhaps a traffic accident?). Without proper status, you’d only be able to work irregular jobs - often these are farm labor, small scale construction work, cleaning services. Those jobs typically don’t require a Harvard degree in any case. Perhaps more importantly for you, if you ever leave the country after overstaying, that will be marked on your file and you’ll be unlikely to be admitted to the US ever again. Workers without visa status are often “trapped” in the US for this reason.