Bernie Sanders, facing a steadily narrowing path to the Democratic presidential nomination, has remained in the race following another disappointing week of primary results and largely pivoted his campaign operation to focus on the coronavirus pandemic.

The Vermont senator has been prevented by the outbreak from holding the massive rallies that were his signature for much of the past year, and he returned to his home in Burlington, Vt., after voting Wednesday in the Senate. The day before, he lost by significant margins in...