It’s counterintuitive to think that old vaccines created to fight very different pathogens could defend against the coronavirus. The idea is controversial in part because it challenges the dogma about how vaccines work.

But scientists’ understanding of an arm of immunology known as innate immunity has shifted in recent years. A growing body of research suggests that live vaccines, which are made from living but attenuated pathogens (as opposed to inactivated vaccines, which use dead pathogens) provide broad protection against infections in ways that no one anticipated.

“We can’t be certain as to what the outcome will be, but I suspect it’ll have an effect” on the coronavirus, said Jeffrey Cirillo, a microbiologist and immunologist at Texas A&M University who is leading one of the B.C.G. trials. “Question is, how big will it be?”