MIAMI — They were some of the most feared people in South Florida, men who became cinematic fodder and, long before Donald Trump uttered the term “bad hombres,’’ ones who really did give some immigrants a bad name.

For almost 40 years, they were also pawns in the cold war between the US government and Fidel Castro: once and future criminals who joined a mass flotilla of refugees that left Mariel Harbor and landed on Florida’s shores, then bedeviled Miami and other US cities that had taken them in.

The United States did not want them. Nor did Cuba, which refused to take them back.

On Thursday, President Obama announced the immediate end of the “wet-foot, dry-foot’’ policy, which allowed Cuban migrants to stay in the United States if they reached its shores.

The flip side of the deal got far less attention, but it effectively closed one chapter in the tortured relationship between the two countries: Cuba agreed to take back up to 500 criminal Mariel refugees.

They arrived as young, often brash young men. Now they are middle-age or even older, possibly years removed from their last crimes. Officials who once reckoned with them, though, do not remember them kindly.

“They were street urchins with bad intent,’’ said Jim Shedd, a former DEA agent in Miami. “Within two weeks of getting here, some of them were working for dopers, bringing in loads and doing rip-offs.’’

The Cuban exodus began in 1980, when Castro opened the port at Mariel for people who wanted to leave, and over a period of months 125,000 Cubans did. Most were law-abiding, but the Cuban leader had opened prison and mental institution doors, too, and within a few years, almost 3,000 of the refugees were in US jails after committing new crimes.

Frantic city officials around the nation set up task forces and committees to study the “marielitos.’’ The term became associated with criminals for a time, which stigmatized others who came on the boatlift, a situation not helped by the movie “Scarface,’’ in which Al Pacino plays a Mariel refugee who becomes a coldblooded Miami drug lord.

Las Vegas determined that 550 of its 2,000 refugees were career criminals, and Los Angeles said that two-thirds of its Mariel immigrants had been arrested within a few years of arrival.

In Miami, which cocaine and turf wars had turned into one of the most dangerous places in the United States, court officials found that half the people found incompetent to stand trial because of mental illness were Mariel refugees.

The Cuban government eventually agreed to take back 2,746 of the criminal Mariel refugees. But the deportations were slow and in some years did not take place at all. At one point, prisoners who had been awaiting deportation for years rioted in several cities.

In 2005, the Supreme Court ruled that the government could not indefinitely detain Mariel refugees who committed crimes but whom Cuba refused to take back. Since then, many have been set free at the conclusion of their prison sentences.

Nearly 250 of them have died, and, by June, 478 of the original 2,746 to be deported remained in the United States, according to Immigration and Customs Enforcement.

Those, however, are not necessarily the ones who will be deported under the Obama administration’s deal with Cuba. Some are elderly or very ill, and the US government has lost interest in deporting them, said a senior Department of Homeland Security official.

In their place, Cuba has agreed to accept other Mariel refugees who have been convicted of crimes in the United States but were not part of the group ordered deported.

The official said the US government had not yet begun making a list of whom to send back; it was also unclear how they would go about rounding up those who have been living freely for years.

Pat Diaz, a former Miami-Dade County homicide detective, said he thought authorities would have a difficult time tracking down people who committed crimes so long ago, though some of the most serious ones are still incarcerated.

Diaz recalled the case of a 20-year-old Mariel refugee who in 1981 killed one cabdriver, shot and robbed another, and shot a friend in the eye during an argument.

“He was vicious,’’ he said. “He was bad news. They should ship him back.’’