The fear is they could lose their jobs if they are exposed or become infected, and have to take sick time.
Texas State Employees Union vice president Joe Montemayor is asking for extended protection for workers, specifically expanding the sick leave pool.
Montemayor says state employees have to earn sick time. "For instance Health and Human Services, some offices are 50% in training. So 50% brand new employees that have not yet earned enough time to take off and be quarantined. If they get sick there's no guarantee their job will be waiting for them when they get back."
Members of his union are on the front lines fighting the virus. They include staffers who work in public hospitals, state supported living centers as well as the big public health universities like MD Anderson, UT Southwestern Medical Center, Health and Human Services Commission and the Department of Family Protective Services.
A news conference is being hosted by the Texas AFL-CIO in Austin.
Unions for teachers, nurses and flights attendants will also be represented.