The incident is under investigation by the US Border Patrol, Texas Department of Public Safety, Dimmit County Sheriff's Office, Homeland Security Investigations, and Customs and Border Protection's Office of Professional Responsibility, Border Patrol said in a statement.
The vehicle rolled over several times as it ran out of control, Ms Boyd said.
The driver and passenger are USA citizens and are likely to face state and federal charges, Boyd said.
A criminal complaint said the driver in that case admitted to investigators that he traveled from Laredo to San Antonio.
Dimmit County officials confirmed Sunday afternoon that five people have died in a crash involving undocumented immigrants.
Boyd said the driver was known to police, and had been seen in the area 'last week, ' either scouting the area or looking for immigrants to smuggle.
Republican Sen. John Cornyn, from Texas, spoke on the Senate floor Monday about the crisis at the border, promising to reintroduce bipartisan legislation he first introduced in 2014 that he said will allow families to stay together.
US Border Patrol said three cars were allegedly involved in smuggling immigrants who they believe had been living in the country illegally. The driver was among those hospitalized and he and the passenger were in custody. The agent radioed a description of the two fleeing vehicles to other agents, according to the statement released by CBP on Sunday evening.
Two vehicles pulled over, but the third sped away, tearing down Texas Highway 85 at speeds of more than 100 miles an hour.
A total of 14 people were in the vehicle, including the driver, who was not seriously hurt. Gayle King asked the right question of Manuel Padilla, the man running the Customs and Border Patrol sector that accounts for the most illegal crossings and detentions, even if the CBS This Morning host didn't get the answer she wanted. "There needs to be censors, there needs to be other things integrated to be able to protect our borders". "This is a ideal example of why our borders need to be secure". The deadly wreck comes amid widespread protests over President Donald Trump's immigration policies that include separating undocumented children from parents caught sneaking them into the country.
A two-year-old Honduran asylum seeker cries as her mother is searched and detained near the U.S. -Mexico border on June 12, 2018 in McAllen, Texas.
"Every day, my deputies are getting into pursuits", he said.