Across New York State, medical providers in recent weeks had the same story: They had been forced to throw out precious vaccine doses because of difficulties finding patients who matched precisely with the state’s strict vaccination guidelines — and the steep penalties they would face had they made a mistake.

On Saturday, state health officials responded to the outcry over discarded vaccines by again abruptly loosening guidelines as coronavirus cases continued to rise.

Now, medical providers can administer the vaccine to any of their employees who interact with the public if there are extra doses in a vial and no one from “the priority population can come in before the doses expire,” the new guidelines read. A pharmacy’s “store clerks, cashiers, stock workers and delivery staff” could qualify, the guidelines said. California last week took a similar step.