When a cold war winds down, what happens to its spies and traitors? The British double agents Kim Philby, Guy Burgess, and Donald Maclean were able to see out their days in Moscow while it was still ruled by Communists, without fears that their hosts might betray them and send them back to an unforgiving Great Britain.

Other scenarios, such as that of the United States and Cuba, are more complicated. On December 17, 2014, the same day that the United States and Cuba announced the restoration of diplomatic relations, an exchange of long-imprisoned spies and double agents also took place. Three Cuban sleeper agents who had been imprisoned in the U.S. since 1998 were released from U.S. federal prisons and flown home. Simultaneously, Rolando Sarraff Trujillo, a C.I.A. double agent who had been held in a Cuban prison since 1995, was flown to the U.S., as was Alan Gross, a State Department contractor who was arrested in 2009 for smuggling Internet equipment onto the island for dissident groups.

But the fates of many fugitive citizens who were given refuge in the United States or Cuba remain in limbo. Among them are people sought back home for crimes including murder, kidnapping, bank robbery, and terrorism. Curious about such people, I recently asked an American official what prevented the U.S. government from arresting, and possibly extraditing, Luis Posada Carriles, an eighty-eight-year-old Cuban exile living in Florida, on terrorism charges.

Posada, a former C.I.A. operative who spent most of the past half century involved in efforts to violently destabilize the Castro government, has been on the top of Cuba’s most-wanted list for decades. I ticked off the long list of his alleged crimes—most notably, the bombing of Cubana de Aviación Flight 455, in 1976, which killed all seventy-three passengers onboard, and a number of bombings and assassination attempts across the Western Hemisphere. As recently as 1997, Posada admitted to planning the bombing of a Havana hotel, which killed an Italian tourist.

The official listened calmly, nodding his head as I spoke. Eventually, he told me, “The complication is that Cuba is also harboring people that the United States would like to see face justice back home.” He mentioned Joanne Chesimard, who goes by the name Assata Shakur, the aunt of the late rapper Tupac Shakur and a former member of the Black Liberation Army, a short-lived offshoot of the Black Panther Party that was devoted to armed struggle.

Shakur, a native New Yorker, has been living in Cuba since 1984. She arrived there after several years on the lam, following her escape from a prison in New Jersey, where she was serving a life sentence for the 1973 murder of a U.S. state trooper. (She was also tried for but not convicted of crimes including bank robbery, kidnapping, and other murders.) Shakur was granted political asylum in Cuba, where she was given a job and a home. She is now sixty-nine, remains on the F.B.I.’s Most Wanted list, and is the undisputed doyenne of the estimated seventy-odd American fugitives living in Cuba. Her 1987 memoir, “Assata: An Autobiography,” whose cover features a photograph of her looking over her shoulder at the camera, can be found in many of Havana’s state-run bookstores, alongside books about Che Guevara and Fidel Castro.

Most of the American fugitives in Cuba are radicals of Shakur’s era. Charlie Hill, who is in his mid-sixties, was a member of a militant group called the Republic of New Afrika, which sought to create an independent black nation in the American South. Hill was accused, with two comrades, of killing a policeman in New Mexico in 1971. Several weeks later, the three men hijacked a passenger plane to Cuba, where they were granted asylum. Both of Hill’s comrades have died, but he remains in Havana. And there is the Columbia University graduate Cheri Dalton, who goes by Nehanda Abiodun, also a veteran of the Republic of New Afrika. Abiodun is sought for her involvement in the armed robbery of a Brink’s armored truck in New York in 1981, in which two policemen and a security guard were killed. She is also thought to have helped Shakur break out of prison. Abiodun, who either fled to Cuba with Shakur or followed shortly after, has reinvented herself there as a mentor to rap artists.

Through the years, I’ve met several of the American fugitives in Cuba. One of them, the quiet and unassuming William Lee Brent, was the bodyguard of the Black Panther leader Eldridge Cleaver. After a 1968 shootout with police in San Francisco, Brent hijacked a jet to Havana, where he went on to teach English in elementary and secondary schools. When I met him, back in the nineteen-nineties, he expressed a bittersweet nostalgia for life in the United States. Not long afterward, he wrote a memoir, “Long Time Gone,” about his life on the run. Brent died, of pneumonia, in 2006.

I also ran into Robert Vesco, a flamboyantly wealthy American financier who became an outlaw, in 1973, after the S.E.C. accused him of robbing a mutual fund of over two hundred million dollars. Vesco moved between the Bahamas, Nicaragua, and Costa Rica before fleeing to Cuba, in 1983. Before long, he was rumored to be assisting the Castro government with its international financial dealings. When I saw him, one day in 1994, we were the only two people waiting at a baggage carousel in a tiny room in the Havana airport terminal for Caribbean flights. I’d been advised by Cuban officials not to show any interest in him, and so I tried my best not to make eye contact. He seemed to have similar concerns, and discreetly moved behind a nearby pillar.

Another day, I met Vesco’s wife and two sons after giving a talk at an international school in Havana. She and her boys came up to thank me for my talk, and we chatted for a while. They went by the last name Quinn, and had Costa Rican passports, but the faculty at the school knew who they really were. Shortly after that, Robert Vesco fell afoul of the Cuban authorities. In 1995, he was arrested, on suspicion of being a spy; he was eventually convicted of “fraud and illicit economic activity” and sentenced to thirteen years in prison. (In a curious twist, Richard Nixon’s nephew, Donald Nixon, Jr., who was visiting Vesco at the time of his arrest and apparently doing business with him, was also arrested and questioned by Cuban authorities, but was later released and allowed to leave Cuba.) Vesco never made it out of prison; he died, of an illness, in 2007, two years short of his release date.

A pair of rogue former C.I.A. agents also saw out their days in Havana. After eleven years of covert service, from 1957 to 1968, Philip Agee was apparently conscience-stricken by what he had seen and done, and became a whistle-blower, publishing a tell-all book, “Inside the Company: CIA Diary,” in 1975. Agee was expelled, under U.S. pressure, from a handful of Western European countries and finally ended up in Cuba. In the years before his death, in 2008, Agee ran a Web site called cubalinda.com, which helped Americans who wished to circumvent the travel ban.