In 2011, developer Koby Kempel paid $2.5 million for a red brick, former carriage house in Boston’s coveted Beacon Hill, one of the priciest neighborhoods in the country. Famed for its cobblestone streets and historic row houses, Beacon Hill has been home to former Secretary of State John Kerry and many other notable Bostonians over the years.

When Mr. Kempel bought the circa-1900 house on Beaver Place, the underground wooden pilings supporting the foundation had been rotting for years, to the point where the building’s...