But the process is usually marred, with ballot language phrased to favor the party in office. In 1998, “none of the above” was the top winner. In 2012, 61 percent of counted votes went to statehood — and half a million ballots were left blank.

But this time, the vote came a few weeks after Puerto Rico declared a form of bankruptcy in the face of $74 billion in debt and $49 billion in pension obligations it cannot pay. More than 150 public schools are being closed as a mass exodus of Puerto Ricans head for the mainland and those who remain brace for huge cuts to public services. Decisions are now in the hands of a bankruptcy judge.

Voters said that Puerto Rico needed the United States now more than ever.

“If there’s an earthquake in Puerto Rico, who is going to send the help? The Americans! This is their land!” said Gladys Martínez Cruz, 73, a retired tax clerk in San Juan’s Barrio Obrero neighborhood. “We need someone who is going to support us, send us money. There’s a lot of hunger in Puerto Rico, even with the help we get.”

Many Puerto Ricans, like Ms. Martínez, live off food stamps, public housing vouchers or other federal programs and worry that a change in political status could affect that aid. A huge publicity campaign warned voters that their citizenship could be at risk.

“I want my children and grandchildren to keep their American citizenship,” said Maira Rentas, a cardiac nurse in San Juan. “Little by little, with whatever votes we get, we have to try to become a state.”

Ana Velázquez, 50, a hospital secretary, said Puerto Rico’s economic problems were so great that they overshadowed other considerations, such as the language, culture and identity that could be lost if the island became a state.

“I don’t want to lose my hymn, my coat of arms, my flag. My beauty queen would no longer be ‘Miss Puerto Rico,’” Ms. Velázquez said. “I don’t see myself ever singing the United States national anthem. I really don’t. But Puerto Rico is in really bad shape, and it needs help.”