Matteo Rocca and Ronan Dunphy peered into the gloom on the second floor of the 12th-century palazzo in Genoa, Italy.

This had once been the grandest part of the seven-story palace, with the highest ceiling, the tallest windows and the most elaborate painted decoration. It was here, on the “piano nobile,” or noble floor, that the aristocratic family who had once occupied the building would have entertained guests.

But by the time the couple saw the former showplace in 2019, it was a ruin. Holes pocked floors and walls. Wind blew in through leaky wooden windows with dingy, rattly glass. The piano nobile lacked basic electricity, never mind heat and running water.

In the 1800s, the palace had been divided into apartments. Then the rear of the building was damaged in a bombing during World War II. The second floor had become a tailor’s shop and residence before the tailor and his family moved out, leaving the space empty for nearly six decades. Even with a cafe and restaurant occupying the ground floor and tenants filling the floors above, the second floor remained dormant, except for a jumble of old furniture and dusty books.

As Mr. Rocca and Mr. Dunphy roved around, it was impossible to discern how the rooms had originally been laid out. They shone flashlights up at the vaulted ceiling of the main room, where a fresco was covered with soot.