JULIA PRESTON

When mothers and children streamed across the Texas border in 2014, the Obama administration devised a strategy to manage the influx, putting them in detention centers to convince others that illegal crossers would be caught and sent back. That strategy is now under intense legal and political attack.

The woman involved in the shootings passed through two rounds of criminal and national security background checks as she obtained a “fiancé visa” and later a resident green card to live in the United States, federal officials said.

The shift marks the first time since immigration from the neighboring nation began to rise in the 1970s that fewer Mexicans came into America than returned home, the Pew report found. The reversal is primarily the result of a steep drop in Mexicans coming into the country.

Many of the visas are given out through a lottery, and a small number of giant global outsourcing companies flood the system with applications, significantly increasing their chances of success.