During the depths of the pandemic, sales at Alo Yoga surged as its popularity exploded on social media. Kendall Jenner appeared on Instagram wearing the brand’s high-waist leggings. Alessandra Ambrosio and Jennifer Lopez were seen in Alo gear, too. In just one year, business reportedly almost doubled, surpassing $1 billion.

Alo’s sister company, Bella+Canvas, a wholesaler of basic apparel, also reached a milestone, selling directly to consumers through its website. To keep up, the two companies turned to a vast new distribution warehouse in Nevada.

Finding workers for such facilities is no small task, but corporate America often looks to a time-tested strategy: contracting with staffing agencies that temporarily employ migrants, including some who enter the country illegally and are desperate for jobs.

This year, America’s southern border was once again a flashpoint in a presidential election, with President-elect Donald J. Trump pledging to deport millions of people who he said were “poisoning the blood” of the country. Within days of his re-election, he announced his intention to appoint hard-liners on immigration.

But despite the tough talk, the broken border has been a lifeline for America’s on-demand economy under both Democratic and Republican administrations, including Mr. Trump’s first term, an investigation by The New York Times found. Thousands of companies have exploited its porousness by plucking workers from the ranks of unauthorized migrants, sometimes with impunity.