They are opening restaurants and bars, fueling start-ups and small businesses or jump-starting moribund sectors, like agriculture. They are motivated both by an urge to help lift Puerto Rico out of its quagmire, but also by a profound attachment to the island — its beaches and countryside, its friendliness, its intimacy and the tug of family.

The pull in the opposite direction can be intense, as Puerto Rico reckons with an economic calamity more than a decade in the making. This island of United States citizens, whose finances are now being overseen by a federal control board, is shackled by around $70 billion in public debt, crushing job losses that are expected to deepen as more government workers are laid off, and an unrelenting exodus that includes many professionals, like doctors, engineers and teachers. Since 2004, more than 400,000 people have left Puerto Rico, a United States commonwealth of 3.4 million people.

As the island enters its 11th year of recession, though, the crisis is slowly giving way to new opportunities that are elbowing aside more conventional ways of thinking. Puerto Ricans have long relied on the government for most of their jobs and on the mainland for many of their careers; university graduates have reflexively looked to United States corporations for work or slid into reliable professions, like medicine or engineering. On the island, they call it the “colonial” mind-set, a way of thinking that is tightly bound to Puerto Rico’s standing as a commonwealth.

“We were taught to be employees here — not entrepreneurs,” said Carlos Cobián, an events specialist who is persuading Puerto Ricans on the mainland to come home, and promoting entrepreneurship on the island.

But that is slowly changing. A younger generation, steeped in today’s entrepreneurship revolution, is starting to think differently.