Caught between a gang of extortionists and the owner of the property where he was working as a construction foreman, they left on a plane with their twin daughters, each carrying little more than a change of clothes.
The couple's three older children, all in their 20s, would follow.
Then came the phone call.
The older children were being held hostage in their home by the landlady, a police officer and several other people who were demanding hundreds of dollars to allow them to leave, even though the rent was paid.
Frantic phone calls brought help, and the family was reunited in Quito, said Leon, tears welling up in his eyes as he recalled his children's terror.
But even here, in Ecuador's apparently peaceful capital city, they do not feel safe.
"It's like an octopus," Barrera said of the organized crime group that forced her family to flee. "They know who you are and where you are. They have an entire organization. They must have people here. We're vulnerable. We're defenseless."
They are not alone. About 1,000 people a month cross the border from Colombia into Ecuador, seeking refuge from armed violence, according to Wilfrido Acuna of Quito's Scalabrinian Mission, which ministers to refugees.
Catholic Relief Services, the humanitarian aid agency of the U.S. Conference of Catholic Bishops, also supports refugee ministry in Ecuador.
Official figures put the number of Colombians in Ecuador at about 170,000, but church workers along the countries' heavily forested river border say it may be closer to half a million.
Negotiators for the Colombian government and the country's largest guerrilla group, the Revolutionary Armed Forces of Colombia, or FARC, have been holding peace talks in Cuba for the past three years. FARC negotiators recently asked to meet with Pope Francis in September when he visits the island.
But a brokered peace is unlikely to staunch the flow of refugees, because many are fleeing extortion, death threats or attacks by criminal bands that grew out of paramilitary groups and are unrelated to the FARC.
"The government's concept of peace isn't the same as the people's concept of peace," Acuna said.
Unlike Leon and Barrera, most Colombians who flee to Ecuador make the journey overland. Last year, Ecuador beefed up its military presence along the border, where there are 75 known points where contraband -- including smuggled people -- crosses into Ecuador, Acuna said.
Sandra Angulo arrived from Colombia's northwestern Choco region in February, unsure of where to go, knowing only that she could not turn back.
Members of a criminal group that had tried unsuccessfully to recruit her teenage son finally abducted him. When a neighbour gave her the news, she ran to the house where he was being held.
"He was tied up and they had beaten him," she said.
His captors assaulted her, too, but she managed to escape with her son.
First she moved her family to a different neighbourhood, but when some of the same criminals showed up there, they fled south into Ecuador, where a sympathetic taxi driver took them to a shelter.
"If it hadn't been for him, we would have slept in the street," Angulo said.
At home, her husband had worked in construction and she ran a shop. Now her husband gets odd jobs, for which he is paid off the books.
Refugees like him are making local economies thrive, but are invisible in Ecuador's workforce, Acuna said.
They are also targets of discrimination. Leon says he was turned down for work when potential employers heard his Colombian accent. Angulo has run into similar problems when trying to rent an apartment.
A number of refugees have settled in Atucucho, a neighbourhood on a hill overlooking Quito where Ricardo Lemos shreds cooked chicken into a plastic container while his wife, Raquel Alvarez, chops onions and cilantro.
Their empanadas -- a pastry-wrapped meat pie -- are always in demand, she said. She makes 40 a day and sells three for a dollar. Rent alone eats up a third of that income, so two of her children also work.
Alvarez said she tried to enroll the children in school, but was told the classes were full. Neighbours later told her that was not true.
Lemos and others were working on the farm his mother had divided up among her children, in Colombia's Antioquia state, when 15 FARC guerrillas showed up. They roughed up the men, raped several women and demanded protection money known as a "vacuna" or vaccination.
Thirty-three members of Lemos' family left that night, including the couple and their five children, who carried just the belongings that fit in a single suitcase. Almost 20 more relatives have joined them in Quito since then.
Now they, like tens of thousands of others, are in a legal and emotional limbo as they wait for their asylum applications to be processed.
The uncertainty takes its toll. Domestic violence is high among refugees, according to a new study. And although they can use the Ecuadorean health system, mental health care is scarce.
Newcomers find their way daily to the Scalabrinian Mission office.
"People think the Colombians who arrive here are poor," says Scalabrinian Sister Leda dos Reis, coordinator of the Quito office. "But they are middle-class people. Many are professionals. They come because they were victims of extortion or because armed groups wanted to recruit their kids."
Many are skeptical of prospects for peace in their country.
"It's a lie," twins Laura and Luisa Leon Barrera said, in unison, of the negotiations in Havana.
And some see no prospects for returning home.
"There are people who haven't gotten out alive," Angulo says. "If I've been given the chance to get out of there, I won't go back. Why go back? They'd kill us."