They work in your restaurants and on your suburban lawns. They labor in your factories and build your homes. They do odd jobs or any jobs. Their children go to your schools and play with your children.

And after years in the United States as immigrants without legal documentation, many of them still live in the national shadows. In New York’s Westchester County, a small group of undocumented parents surfaces one January night at a parish council meeting. Through a translator, Gustavo speaks on behalf of all.

Despite simplistic language that depicts a flood of undocumented migrants crossing the U.S. southern border, migration from Mexico has slowed considerably in recent years and even reversed.

“The fear that we undocumented people have is very great,” he says. “Could a traffic stop mean deportation,” he wonders. What would become of the children left behind?

“I’m not sure how the community can help us in this difficult situation for our families, for our children,” Gustavo says, his eyes scanning the faces of the other members of his parish. “But can you help us?” he asks.

Apprehension rates are trending down despite an uptick in 2016The simple appeal stills the parish meeting room. “If ever there was a time to take a stand, it’s now,” a council member finally says.

Containing undocumented immigration with a border wall and threats to deport millions of people were among President Donald J. Trump’s talking points as a candidate. Now, in the early weeks of his administration, the president is fulfilling commitments that many believed were mere campaign bluster. The fear created by Mr. Trump’s recent executive orders among undocumented families is real, but the urgency of addressing the “problem” of undocumented people may be less so.

Despite simplistic language that depicts a flood of undocumented migrants crossing the U.S. southern border, migration from Mexico has slowed considerably in recent years and even reversed. Apprehensions by the Border Patrol, reported by fiscal year, declined from about 1.1 million in 2006 to just over 337,000 in 2015. They spiked in 2016 to 416,000—with increasing numbers of Central American families and unaccompanied minors picked up.

Numbers from Mexico are declining, while dramatically increasing from Central American states.But even if an immigrant inundation is more rhetorical than real, the question of how to deal with the undocumented people already in the United States remains. The overall number of undocumented immigrants has stabilized in recent years from a 2007 peak of 12.2 million to just over 11 million people.

A little more than half of undocumented residents are of Mexican origin. But from 2009 to 2014, the number of undocumented Mexican immigrants fell from 6.4 million to 5.8 million, according to the Pew Research Center, while those from other nations rose from 5.0 million to 5.3 million, with significant increases from Guatemala, Honduras and the continents of Africa and Asia.

Two-thirds of the undocumented have lived in the United States for more than a decade, representing thousands of families that have inhabited a prolonged limbo. A comprehensive reform package that promised to rationalize U.S. immigration policy, long supported by the U.S. bishops, has moldered in Congress since 2013.

President Obama tried to push immigration policy forward with a mix of record deportations that emphasized enforcement and executive orders aimed at protecting some groups—among them the so-called Dreamers, young adults who were brought as children to the United States without authorization. But his successor appears intent on more punitive measures.

Mr. Trump has pledged to “begin removing the more than two million criminal illegal immigrants from the country,” a number disputed by advocates who say there are no more than 820,000 undocumented people with criminal convictions, many for crimes relating to their lack of status. The End Illegal Immigration Act would imprison anyone who re-enters the United States after having been deported.

Under President Obama, the United States deported a record 2.5 million people. Hundreds of thousands of these deportees left children and family behind, and many have sought to return to them. Under Mr. Trump’s proposed law, they would fill the nation’s prisons.

Over the past decade, as spending on immigration enforcement skyrocketed, budgets aimed at regional stabilization and economic development remained stingy.

What becomes of the children of deported immigrants represents a unique challenge. The Migration Policy Institute estimates that there were 5.1 million children in the United States with at least one parent who was an undocumented immigrant between 2009 and 2013. Overall, about 80 percent of these children—4.1 million—are U.S. citizens themselves. Studies are only now grappling with the psychological and developmental impact on U.S.-citizen children when a parent—most often a father and the primary family earner—is removed from the household because of deportation, and how living with that threat day-to-day affects child development.

Over the past decade, as spending on immigration enforcement skyrocketed, budgets aimed at regional stabilization and economic development remained stingy. Though it committed $142 million, in 2016 the United States actually delivered just $47 million in aid to Mexico, the lion’s share directed to security initiatives and just $4.4 million to economic development. Guatemala received just $57 million in total aid that year; Honduras, $49 million; and El Salvador, $29 million.

That same year the United States spent $19.4 billion on immigration enforcement, and America’s border wall may cost as much as $40 billion.

Kevin Clarke is America’s chief correspondent and the author of Oscar Romero: Love Must Win Out (Liturgical Press).