Soltren pleaded not guilty today in a Manhattan federal courtroom and remanded to jail cell.
There are believed to be dozens of other Americans living in Cuba beyond the reach of U.S. law enforcement. Most of them have been holed in Cuba for decades, with many living casually in plain sight. Others, however, are taking no chances and living deep underground.
The best known American fugitive still hiding out in Cuba is JoanneChesimard, 62, also known as Assata Shakur.
Chesimard, a member of the radical activist organization the Black Liberation Army, was found guilty of first degree murder in the shooting death of a New Jersey state trooper in 1977. She escaped from prison in 1979 and was last seen in Cuba in 1984. She is widely believed to still be living underground in Cuba.
"Chesimard is definitely one of the top people on the list of fugitives," said Camila Gallardo, spokesperson for the Cuban American National Foundation.
The FBI has offered a reward of up to $1 million for information leading to her capture.
"She has been living in Cuba for decades under the protection of [President Fidel] Castro. In the beginning, the fugitives were treated well and he utilized them to thumb his nose at the U.S," she said.
Among the FBI's 10 most wanted fugitives – a list that includes Osama bin Laden – is Victor Manuel Gerena. Gerena has been on the lam since 1984 after being accused of stealing $7 million in the heist of the Wells Fargo armored car depot in Connecticut to finance a Puerto Rican separatist group.
Gerena has the dubious distinction of being second only to one other fugitive for the most number of years spent on the most wanted list.
He is believed to be still living in Cuba, and the FBI has offered up to $1 million for information leading to his capture.
The exact number of American fugitives living in Cuba today remains unknown. Some of them remain on the FBI's Most Wanted List, and most were members of radical leftist organizations, who fled to the Communist-controlled island to escape U.S. authorities in the 1960s and 1970s.
"Most of these guys have been there for a long time," said Wayne Smith, an ABC News consultant and former chief of the U.S. Interest Section in Cuba.
"Many of them, like Soltren, hijacked planes, sought refuge and have been living there ever since. By and large, they've been accepted and live normal lives. They have housing and have been assigned jobs," Smith said.
In 1968, more than 30 planes were hijacked or attempted to be hijacked to Cuba. In addition to the Pan American flight bound for Puerto Rico from New York, which Soltren and two other men hijacked Nov. 24, 1968, two other planes were also hijacked that day.
Many of the fugitives, Smith said, were members of Puerto Rican separatist groups or black nationalist organizations.
Cuba and the United States have had an extradition treaty that dates back to the 1920s. In 1971, the two countries signed a pact that dealt specifically with extraditing hijackers, but few fugitives who arrive on either country's shores have been sent back for trial.
"There are treaties," said Smith. "But the fact is the U.S. hasn't extradited anyone back to Cuba, so they haven't extradited anyone back to us."
While fugitives like Chesimard and Gerena are living deep underground in Cuba, others live normal lives there.
In January, William Potts, a hijacker who arrived in Cuba from New York, gave an interview to CNN in which he said he wanted to return to the U.S. and receive a pardon from President Obama.
Potts served a 13-year prison term in Cuba after he arrived in the country in 1984. Today, he lives with his family on the outskirts of Havana.
Robert Vesco, who Slate magazine called "the undisputed king of the fugitive financiers" was perhaps the richest fugitive to take refuge in Cuba and was one of a few not associated with revolutionary activist groups.
Vesco fled to Cuba in 1982 after a series of allegations brought against him in the U.S. and throughout the Caribbean. He was accused of stealing some $200 million from investors in the 1970s and making an illegal contribution to Richard Nixon's 1972 presidential campaign.
After receiving the protection of the Cuban government, Vesco was sentenced to prison in Havana in 1996 and died from lung cancer in Havana in 2007.
"Many of [the fugitives] have just tried to lay low," said Gallardo. "They hope that if relations improve and if a treaty is worked out, we'll start to exchange folks."