Can my husband receive back pay for working off the clock? What times of proof are needed?

All I can say is "wow".  Sadly this is an all-too-common situation.  Workers are reticient to assert their rights for fear of being fired or subject to adverse treatment at work.  I can assure you that what is going on is not in compliance with Federal or State law. I would encourage your husband to file a complaint with either the U.S. or PA Department of Labor and those agencies may conduct an investigation resulting in back-pay plus penalties for the unpaid hours your husband has worked. Your husband can also retain private counsel to assert his rights under those statutes.  If several of the employees there band together it can reduce the chance of adverse consequences from the employer.  I'd urge you to take action!