“There was a lot of talk that after the end of Title 42 it was going to be very difficult to come to the United States,” said Rosa, 30, who had traveled from Venezuela.

Rosa, her husband and their three young children had recently arrived at the Rescue Mission shelter, where about 220 migrants were staying as of Thursday night. The family had turned themselves in to immigration authorities to seek asylum about a week earlier.

As she spoke, Rosa’s 6- and 9-year-old sons around played circular tables where dozens of migrants had gathered to eat dinner together. The brothers ran over to explore a piano, their experimental music and laughter filling the air. In a nearby room, her 2-year-old daughter slept under her father’s watchful eye.

Rosa, who asked that her full name not be used for fear of immigration reprisals, said she and other migrants were very afraid of possible punishments under Title 8, the section of US law that was in place before Title 42 and is now being enforced again in its absence.

Under Title 8, those who repeatedly attempt to enter the US illegally face penalties, including a potential five-year ban and criminal prosecution. Title 42 had those penalties suspended, which led to an increase in the number of people who repeatedly crossed the border after they had been expelled.

“At the end of Title 42, that would be eliminated, and so that was the fear, not being able to come and turn yourself in,” she said.

Juan José Rivera, 25, a Colombian migrant staying in the area outside the Sacred Heart church, said fear of deportation and punishment “motivated a lot of people to turn themselves in.”

“Sadly, a lot of us were still turned away. But thank God we were allowed to come legally,” said Rivera, who wore sneakers with bright turquoise laces and carried a clear plastic bag containing his immigration documents.