Health Care Workforce Protection Act of 2020 This bill directs the Department of Homeland Security to extend the authorized stay period for certain alien health care workers to until at least 60 days after the end of the declared emergency period stemming from the COVID-19 (i.e., coronavirus disease 2019) outbreak. This extension shall apply to an alien (1) who was admitted into the United States as a health care worker on an H-1B nonimmigrant visa (specialty professions); (2) who served as a health care worker in the United States during the emergency period; and (3) whose employment was terminated during the emergency period, unless the termination was for cause.