LA CRUZ, Costa Rica — In Gretchen López’s slumber, during whatever winks of sleep she could get in a crowded open air shelter, she dreamed she was sending money to her mother in Cuba to renovate her crumbling house and buy delicious food.
“But I woke up and I was here,” she said, looking around a fire station here in rural Costa Rica, where she sleeps beside hundreds of other Cubans who got stuck while trying to make a perilous journey through eight countries to reach the United States.
Now, after two months languishing in a shelter, Ms. López and nearly 11,000 other Cubans who were stranded because of a political impasse in Central America will soon be back on the trail, heading to the United States in an exodus that some officials have likened to a stampede.
While American politicians debate whether to accept Syrian refugees and lament the crush of Central Americans who make their way illegally into the United States, the border is about to be crashed in the coming weeks by another wave of newcomers.
But in this case, the Cubans have a trump card: American law has long given them special status to live in the United States and apply for a green card — provided they make it there.
This latest wave of Cuban migration stems from a number of changes enacted by Cuba’s communist government in recent years, in part to jump-start the island’s feeble economy. People are allowed to sell their cars and real estate, a move that suddenly enabled many more to pay smugglers to get them to the United States. Cuba also began allowing its citizens to obtain passports and leave the country more freely, unleashing a rush for the exits.
If that was the kindling, the Obama administration’s decision in 2014 to restore diplomatic relations with Cuba served as the match. Rumors quickly circulated that with embassies reopening, the United States would soon eliminate the 1966 Cuban Adjustment Act, which gives Cubans who make it to the United States a fast track to permanent legal residency.
“There’s a rush of Cubans now, because a lot of people are afraid of that law being repealed,” said Lázaro Clarke, 34, who worked as a barber and fruit vendor in Havana, as he waited in Costa Rica. “With the law or without the law, I’m going.”
Tens of thousands of Cubans have plunked down the profits of their home and car sales to pay for a treacherous 5,000-mile journey by plane, bus, boat and foot. Most have begun by flying to Ecuador, which did not used to require a travel visa. Then they have moved on to Colombia, Panama, Costa Rica, Nicaragua, Honduras, Guatemala and Mexico in hopes of reaching the American border.
The circuitous route allows Cubans to bypass the dangerous trip through the Florida Straits, a crossing that cost many Cubans their lives and where, because of an American policy known as “wet foot, dry foot,” they would be turned back if caught by the Coast Guard.
About 30,000 Cubans made it to the southwest border of the United States in the 2015 fiscal year, a 77 percent increase from the year before, according to the Customs and Border Protection agency.
Kathya Rodríguez, the director of Costa Rica’s immigration service, said, “In 2015, the numbers just shot up.”
Costa Rica said it warned its neighbors last year that a tidal wave was building.
“Many countries turned to look the other way, as though they were ghosts — they knew they were there, but paid no attention,” said Costa Rica’s foreign minister, Manuel González.
Then in November, Costa Rica broke up a smuggling network that had been ferrying migrants through the country. Without the guides to lead the way, migrants who had been quietly slipping past border crossings suddenly became conspicuous. Thousands of them.
Costa Rica gave them transit visas and sent them on their way, but Nicaragua — a longstanding ally of Cuba — balked, refusing to let them pass. Cubans started to pile up at the Nicaraguan border. In November, throngs of them pushed their way past the border agents.
They were repelled by Nicaraguan soldiers with tear gas and swift beatings. “As much as we lived under a regime, nothing like that had ever happened to us before,” Ms. López, 22, said. “Tear gas? Bullets? Some of us had been beaten by the police before, but not like that.”
Thousands of Cubans who said they were fleeing political and economic repression at home learned about the unexpected perils of free societies, including the proliferation of guns. Armed bandits preyed upon Cubans on the road, especially those who had not thought to first wire their life savings to relatives in the United States.
“I would tell anyone not to take this trip,” said Pedro Enrique Duarte, a 48-year-old accountant who was attacked in Colombia and rescued by a local family. “You spend the whole time straddling between life and death.”
Many people were financially wiped out.
“I sold my house for $3,000, and I will arrive in debt,” said Dayana Fernández, a 22-year-old hairdresser who hopes to join her in-laws in South Florida.
With Nicaragua still refusing to offer passage, Costa Rica has spent $1 million to house and feed the Cubans in schools and other shelters around the country.
“Never before have we, even in a natural disaster, had the necessity to attend to this many people for this long,” Mr. González said.
Late last month, Costa Rica and the other Central American countries agreed on a plan to hasten the Cubans’ departure. On Tuesday, a group of 180 Cubans are scheduled to fly over Nicaragua to El Salvador, which had not been part of the migrant trail. From there, they will take a bus to Guatemala, then another to southern Mexico.
If the effort goes smoothly, two flights will leave each day, with the expectation that it will take three weeks to evacuate the approximately 8,000 Cubans stuck in Costa Rica. The hope is to hatch a similar plan for the 3,000 Cubans in Panama, too.
The Cubans will pay $555 for the charter flight, the bus and food arranged by a travel agency. Once in Mexico, the Cubans will be on their own to reach the United States border. Unlike Hondurans and other Central Americans trying to reach the border, Cubans can receive a 20-day transit visa from Mexico.
Nations in the region stressed that the deal was a one-time offer. To stem the flow of migrants, Ecuador started requiring visas in December. Costa Rica says it will deport any additional Cubans caught in its territory.
The Cuban government has long condemned the American policy of accepting Cuban migrants, saying it encourages human trafficking and “the politicization of immigration policies.”
“We see it as a double standard,” said Hugo Martínez, El Salvador’s foreign minister. “It’s a policy that allows one set of migrants to be treated in a privileged manner and another set of migrants in a discriminatory fashion.”
There has been ample talk of modifying or revoking the 1966 Cuban Adjustment Act, but the likelihood of action by Congress appears slim.
“Nobody should be given preferential treatment,” said Representative Henry Cuellar, a Texas Democrat who visited the Cubans at the shelters in Costa Rica. “I don’t think it’s fair at all.”
Even some staunch opponents of the Cuban government say the law needs to be rethought.
“This notion that you’re going to have people coming up Central America and into the United States through the southern border is unacceptable,” said Senator Marco Rubio of Florida, a Cuban-American running for the Republican presidential nomination.
The State Department said in a statement that the United States is “committed to supporting safe, orderly and legal migration from Cuba,” but added that “the administration has no plans to alter current migration policy regarding Cuba.”
The only bill to repeal the act came from Representative Paul Gosar, Republican of Arizona, who said Cubans should be treated like other “illegal immigrants.” He drew little support from Cuban-Americans, and his bill has gained little traction.
“Maybe people think it’s not fair for us to get that privilege,” said Igor Thondike, who has been sleeping on a basketball court in Costa Rica since November. “It’s also unfair that we Cubans have gone more than 50 years without an election.”
He is eager to continue his journey and hopes to find a job installing windows in the United States.