Leonardo Ciaccio, mayor of Sambuca in Sicily, put 16 houses up for auction at a starting price of €1 early this year as part of an effort to halt the depopulation of his small town. Within weeks, more than 100,000 people, mostly from the U.S., requested information.

“We had to hire people who speak English,” Mr. Ciaccio said. “At some point, we were joking in the office that there was no point in answering the phone: Nobody calling spoke Italian.”

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