But Hearst, whose fortune was dented during the Depression, ultimately abandoned the project and gave the monastery to San Francisco. The city’s plans to use it as part of a museum of medieval art in Golden Gate Park went nowhere. The crates containing the stones caught fire in the park a couple of times, and the stones were left to the elements.

In 1979, an art historian, Margaret Burke, participated in San Francisco’s last attempt to restore the monastery. For four years, Ms. Burke inspected the stones to determine what could be saved.

“I found that the chapter house was the only building that would be feasible to rebuild,” Ms. Burke recalled.

The city, though, could not raise the money for the project.

Over the decades, the monks here had watched the situation with growing despair. A chapter house serves as the heart of an abbey, the place where monks gather daily for readings and meetings. What’s more, Cistercian architecture, in its simplicity and austerity, was a reflection of the order’s faith.

“Our architecture was considered part of our prayer, and it still is,” Father Schwan said. “It’s not just the matter of a building. It expresses that vision of what we desire to strive for in our relationship with God.”