(CNN) Laura Vianelo remembers the stories of young Cuban migrants who "threw themselves at the sea," only to die in a desperate attempt to set foot on American soil.

So, she applauded the Obama administration's abrupt end to the longstanding policy, known as "wet foot, dry foot," by which the US sent back Cubans intercepted at sea but allowed those who reached land to stay.

The policy encouraged Cubans to risk their lives to seek freedom and enter the US without a visa to become permanent residents, Vianelo said.

"It is now up to the new generation, the young Cubans, to liberate themselves from communism the way it's supposed to be done, from inside Cuba," Vianelo said.

She was among scores of Cuban-Americans who gathered Thursday at the popular Versailles Restaurant in Miami's Little Havana neighborhood to discuss the policy change. Some expressed displeasure. Others said the change could ultimately be a boon for the island nation.

The policy had applied solely to Cubans. An even less restrictive "open door" policy for Cubans was established by President Lyndon B. Johnson in the 1960s. But in the 1990s -- following a mass exodus of Cubans to the United States -- President Bill Clinton amended the rule to state that the US would send back seafaring Cubans who hadn't yet reached US soil.

Because Clinton's "wet foot, dry foot" policy still allowed visa-less Cubans to stay if they reached land, other immigrants, including Haitians, have long criticized it. Non-Cubans who enter the country without a visa generally are arrested and deported.

People look at a Cuban migrant boat that brought 12 people and a dog to the beach on September 15, 2015 in Miami Beach, Florida under the previous wet-foot, dry-foot policy.

Treating Cubans like other migrants

Orlando Silva, a Miami doctor who fled Cuba with his family and never went back, said the policy change "is another betrayal by this country" that favors communism.

The United States has "always been against this country," he said of his native homeland.

A senior administration official said the US Department of Homeland Security would eliminate the policy that made Cuban nationals eligible for resident status within a year.

Immediately, Cubans "who attempt to enter the United States illegally and do not qualify for humanitarian relief will be subject to removal, consistent with US law and enforcement priorities," the White House said in a statement.

"By taking this step, we are treating Cuban migrants the same way we treat migrants from other countries," the statement said.

Snapshot: Cuban migration Prompted in part by fears that thawing relations with Cuba will end favorable U.S. policies, thousands of Cuban immigrants are trekking through Latin America on their way to the United States. Here's a snapshot of other countries involved: Ecuador was once a magnet for Cuban migrants because the South American country didn't require entry visas. That practice ended last year, and many Cubans are leaving with the threat of deportation looming. Nicaragua in Central America closed its border to Cubans heading north last year, leaving thousands stranded to the south in Costa Rica. Costa Rica struck a deal in January to begin airlifting Cubans out of the country, then closed its borders to stop more from coming in. That left thousands stranded to the south in Panama. Panama began humanitarian airlifts in May that sent more than 3,100 stranded Cubans north to Mexico at the U.S. border. Now Panama's borders are closed, too. Mexico gave Cubans arriving on flights from Central America temporary papers and shuttles them to the U.S. border. Colombia says it will deport Cubans stranded there to avoid setting a precedent and facilitating human trafficking.

Medical parole program also eliminated

Cuba's government also agreed to accept Cuban nationals who have been ordered removed from the United States, just as they had accepted migrants intercepted at sea under the "wet foot, dry foot" policy, the White House said.

The Department of Homeland Security also eliminated a policy for Cuban medical professionals known as the Cuban Medical Professional Parole Program, a senior administration official said.

Miami-Dade County, Florida, Mayor Carlos A. Gimenez, whose county boasts a large Cuban-American population, said he was disappointed by the decision to end the medical parole program.

"The duties of the doctors who were previously protected by this program will continue to be mandated by the Cuban dictatorship," Gimenez said in a statement. "These doctors have been used as instruments of the regime and sadly, the elimination of the program will negatively impact their ability to practice medicine freely.

Gimenez also said eliminating the "wet foot, dry foot policy" would "undoubtedly impact" the Cuban-American community. But while the old policy granted relief to many fleeing persecution, the mayor said he was concerned it "was being abused and required adjustments."

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Family Reunification Parole Program unaffected

Federal officials said the DHS is also eliminating an exemption that had prevented the use of expedited removal proceedings for Cuban nationals apprehended at ports of entry or near the border.

The existing Cuban Family Reunification Parole Program, which allows certain eligible US citizens and lawful permanent residents to apply for parole for their family members in Cuba, is unaffected, the official said.

The "wet foot, dry foot" change was likely to be Obama's last move in his historic dealings with Cuba, In 2014, Obama reopened ties to the island nation after a half century of frozen diplomatic ties.

Photos: President Obama visits Cuba U.S. President Barack Obama attends a baseball game in Havana, Cuba, with his family and Cuban President Raul Castro, right, on Tuesday, March 22. The Cuban national team was playing an exhibition against Major League Baseball's Tampa Bay Rays. Obama is the first U.S. President to visit Cuba since Calvin Coolidge in 1928. Hide Caption 1 of 19 Photos: President Obama visits Cuba Tourists in a Havana antique shop watch Obama give a speech on March 22. Hide Caption 2 of 19 Photos: President Obama visits Cuba Obama waves to the crowd before delivering his speech at the Grand Theater in Havana on March 22. In his speech, Obama urged Cubans to look to the future with hope, casting his historic visit as a moment to "bury the last remnants of the Cold War in the Americas." Hide Caption 3 of 19 Photos: President Obama visits Cuba First lady Michelle Obama and her daughter Malia stand with children of U.S. Embassy workers after dedicating a bench and two magnolia trees at a small park in Havana on March 22. Hide Caption 4 of 19 Photos: President Obama visits Cuba The Obamas pose with Castro before a state dinner in Havana on Monday, March 21. Hide Caption 5 of 19 Photos: President Obama visits Cuba U.S. Secretary of State John Kerry, right, speaks with Cuban First Vice President Miguel Diaz-Canel ahead of the state dinner on March 21. Hide Caption 6 of 19 Photos: President Obama visits Cuba Castro tries to lift up Obama's arm at the end of a joint news conference on March 21. Hide Caption 7 of 19 Photos: President Obama visits Cuba Obama meets with Castro in Havana on March 21. Hide Caption 8 of 19 Photos: President Obama visits Cuba Michelle Obama speaks with Cuban girls during a Let Girls Learn roundtable in Havana on March 21. Hide Caption 9 of 19 Photos: President Obama visits Cuba Obama lays a wreath at the Jose Marti monument in Havana's Revolution Square on March 21. "It is a great honor to pay tribute to Jose Marti, who gave his life for independence of his homeland," Obama wrote after he laid the wreath. "His passion for liberty, freedom, and self-determination lives on in the Cuban people today." Hide Caption 10 of 19 Photos: President Obama visits Cuba Backdropped by a monument depicting revolutionary hero Che Guevara, Obama listens to the U.S. national anthem during the wreath-laying ceremony on March 21. Hide Caption 11 of 19 Photos: President Obama visits Cuba Obama and Castro review troops before bilateral meetings on March 21. Hide Caption 12 of 19 Photos: President Obama visits Cuba Obama walks up the stairs of the Palace of the Revolution on March 21. Hide Caption 13 of 19 Photos: President Obama visits Cuba Obama and members of the first family take a walking tour of a Havana cathedral on Sunday, March 20. Hide Caption 14 of 19 Photos: President Obama visits Cuba The first family stops to look at a painting of Abraham Lincoln in the Museum of the City of Havana on March 20. Hide Caption 15 of 19 Photos: President Obama visits Cuba Obama's convoy drives along the Malecon sea wall on March 20. Hide Caption 16 of 19 Photos: President Obama visits Cuba The President and first lady greet families of embassy personnel on March 20. Hide Caption 17 of 19 Photos: President Obama visits Cuba Obama waves shortly after arriving at Jose Marti International Airport. Hide Caption 18 of 19 Photos: President Obama visits Cuba Obama and his family exit Air Force One on March 20. Hide Caption 19 of 19

Could real change now come to Cuba?

In November, Cuba's longtime leader Fidel Castro died at age 90. Castro's younger brother, Raul, who had been running the island nation for more than a decade, plans to step down in 2018.

Music producer Armando Flores, a second-generation Cuban, said the "wet foot, dry foot" policy was "an escape valve" for Cubans under the Castro regime. But the policy change may bring out transformation of the government, he said.

"Lots of things can happen, like a rebellion or a bigger focus on these Cubans that want to make a profound and real change in Cuba now that this bridge isn't there... there's no escape," he said.

But Flores said it is now "unfortunate for those who really come to the US looking for liberty and ... find themselves in this situation."