"The federal buyout program never anticipated a whole community being bought out, but the utter devastation of our area called for that," said Mr. Tirone, who is now running for state Assembly.

To sweeten the deal, Mr. Cuomo created an "enhanced zone" within the buyout program that included a 10% cash bonus for homeowners who participated. It worked. "People on the fence about selling just put blinders on and took the opportunity to get out," said Mr. Tirone. Their neighborhood on Staten Island's southeastern shore today looks somewhat post-apocalyptic. Some lots are empty. Others are in various states of decay. The remains of a white-shingled house on Kissam Avenue sags in on itself behind an orange plastic fence. Six-foot-tall reeds encroach upon it from either side, brushing the boarded-up windows in the gentle breeze coming off the nearby Atlantic Ocean. With the state cutting checks for dilapidated houses and Oakwood Beach's transformation moving ahead, it didn't take long for people in other hard-hit areas to start asking about selling out. "I thought what happened over there was great, but it was hard for me to appreciate that while my own neighborhood was still totally destroyed," said Frank Moszcynski, a resident of Ocean Breeze, just a mile and a half north of Oakwood Beach. Residents there said that city officials who went on to establish the Build It Back program came to Ocean Breeze in November 2012 and pledged to buy back homes, but only at reduced, post-storm prices. It was not a great deal, but it was better than nothing. "They said they'd be back tomorrow with paperwork to get things started," Mr. Moszcynski recalled. "Tomorrow never came." Joe Herrnkind—a neighbor of Mr. Moszcynski who was unable to get back into his house for three days and who discovered that the floodwaters had gone as high as his attic—was similarly frustrated by what seemed to be the city's ham-fisted response. In the spring of 2013, they formed the Staten Island Alliance, a community group focused on getting relief for the area around Ocean Breeze. Inspired by what had been done at Oakwood Beach, Mr. Moszcynski inquired about the state buyout program, only to be told by a local city official, "I think we can both agree that ship has sailed."