Student visas allow for work up to 3 years after graduation in STEM fields like mine. Virtually all employers in my field have dedicated staff whose sole job is to verify that employees have proper work authorization in compliance with Federal regulations.
I can tell you that in 15+ years of working in my industry, including for some of it's largest companies, that I have never heard of anyone working on an expired visa of any type. Employees have to provide copies of work authorization documents whem they are hired and expiration dates are tracked. If those dates pass and authorizations aren't renewed, the employee is immediately terminated. If not, the company would get a big fine and possibly lose customer contracts.