When Juliana Garcia crossed the U.S.-Mexico border with her 8-year-old daughter, Glendy, in December, she hoped to find safety and build a new life with her father living in Tennessee.

But Ms. Garcia and her daughter remained in the U.S. just 25 days before being returned to Guatemala. Based on where they crossed the border, near El Paso, Texas, the two were placed in an experimental Trump administration program designed to give asylum seekers brief and rapid access to the U.S. legal system—and deport them quickly if the government finds they don’t qualify for protection.

A review of the Garcias’ case provides a rare look at the program’s structure, which has processed several thousand people to date, and the hurdles it presents for asylum seekers and their lawyers.

The program, known as the Prompt Asylum Claim Review, or PACR, streamlines the process of applying for asylum so that applicants receive a decision in a matter of days, rather than the months or years it typically takes for a case to work its way through the backlogged immigration-court system.

The U.S. government quietly launched the PACR program in El Paso in October and is expanding it across the southern border this month.