Meanwhile, the Tenement Museum is trying to keep the trains running, including maintenance of its two Orchard Street properties, one of which still has a few tenants. “The last thing we’re going to do is leave those buildings to the elements,” Mr. Vogel said.

Though Mr. Vogel, 74, is in a high-risk category for the virus, he still goes into the museum once every other week to sign checks. Having served as president from 2008 to 2017, he came out of retirement last fall to serve on an interim basis, while the museum searches for someone permanent.

Even as he cuts costs, Mr. Vogel is focused on beefing up the museum’s online programming, with a digital exhibit on the census, for example. It offered a live craft-making program for children “inspired by the resourcefulness of former tenement residents.” And on Wednesday it will present “A Nickel for a Pickle“ on YouTube, “a journey into the history of pickles on the Lower East Side,” including “a short demo of how to make your own cucumber pickles at home!”

With schools closed, the museum has also been pushing out educational materials to thousands of teachers, drawing on the expertise developed for tours like “Life and Death at the Tenement,” developed in 2018, which explores past epidemics like cholera, yellow fever, tuberculosis and AIDS.

Mr. Vogel happens to be familiar with pandemics; he spent most of his career as a historian of medicine and is particularly attuned to how viruses are sometimes attributed to “outsiders.” The Federalists in 1793 blamed Philadelphia’s yellow fever on French-speaking refugees fleeing a slave revolt in Santo Domingo, he said. In 1892, Jews were held responsible for bringing typhus and cholera to New York.

“Immigrants were seen as disease carriers,” he said.

In this period of adversity, Mr. Vogel said, he is strengthened by a bedrock faith in the institution’s mandate. “A lot of what makes us strong as a people came from the strength immigrants found in themselves,” he said. “It’s important to focus on that.

“I have absolute conviction that what we’re doing is essential,” he continued. “We may have to do it online, we may have to rely on philanthropy instead of earned revenue, we may have to do it with a smaller staff. But we’re going to do it.”