(Alyssa Schukar | The New York Times) A woman sweeps at an encampment in Matamoros, Mexico, which is home to hundreds of migrants seeking asylum in the United States, on Nov. 7, 2019. A federal court on Friday, Feb. 29, 2020, upended a central pillar of the Trump administration’s immigration agenda, ruling that asylum seekers must be allowed into the U.S. while their often lengthy cases meander through American immigration courts.