For many of the families, the free meals were not the difference between their children eating or not eating. Instead, they said they viewed it as a way to stretch their budgets a little longer, so that the money they would have spent on that day’s lunch could instead go to tomorrow’s dinner or next week’s bill. Word had spread while families idled in line that the Texas governor was activating the National Guard, that some of the shelves at a local grocery store were still barren. The drive-through at Alton was one small bright spot at an anxious time, even though their county had no confirmed cases of the coronavirus.

Gabbie Salazar, 28, made two trips to the drive-through, each time with different sets of nieces, nephews and cousins in her car. She knows Alton well: She manages the school cafeteria. She is a single mother who works two jobs, at the school and at a day care, and makes a total of about $2,000 a month, with a rent of about $800 monthly.

“Save a little money, you know?” Ms. Salazar said of the free meals. “I’m a single mom. I only have to do one meal at night, so that helps a lot.”

Before Ms. Mossbarger pulled up in the drive-through line on Tuesday, she took her six children to the H-E-B grocery store. She went to the aisle for paper towels and toilet paper, but there was nothing left — the shelves were empty, and customers were crowding around to grab whatever they could. She gathered the children, left the cart in the middle of the aisle and walked out, frustrated that she had wasted gas in her Chevrolet Suburban.