Sam Hawgood, the chancellor of the University of California, San Francisco, was getting concerned.

It was March 19, coronavirus cases in California were rising at an alarming rate, and U.C.S.F., one of the Bay Area’s major medical providers, was already running perilously low on personal protective equipment.

The university’s usual suppliers in the United States were short on masks and face shields, and there was no sign that the State of California or the federal government was coming to the rescue. “The supply chain had really dried up,” Mr. Hawgood said.

So Mr. Hawgood called Marc Benioff, the hyperconnected billionaire who is a founder and the chief executive of Salesforce.

In some ways, it was the natural call to make. Mr. Benioff gave the university $100 million to build a children’s hospital in 2010 and remained a major benefactor. But there was no reason to think Mr. Benioff, who runs an enterprise software company, could quickly muster a supply chain for personal protective equipment, especially during a global pandemic.