HOUSTON — When I was a child in the 1960s in San Antonio, agents from the Immigration and Naturalization Service showed up at our house. “La migra,” as we called the I.N.S. in Spanish, was a term that carried an edge of anxiety, though I didn’t quite understand why. I just knew that I wasn’t to open the door to anyone in uniform, and that there were certain bus stops our housekeeper, Juana, avoided.

But even with all the precautions, a man in a khaki shirt and sunglasses eventually knocked on our door, asked for Juana by name and carted her away. This happened a couple of times, but within weeks, she would be back at work.

This cat-and-mouse game was common in San Antonio back then, because once a Mexican immigrant hit town, he or she could find plenty of work as a nanny, a maid, a restaurant dishwasher, a landscaper, a road builder — as the cliché goes, pretty much everything that other people wouldn’t do, or wouldn’t do for the wages offered.

The pay was lower than minimum wage, and health benefits, if they existed at all, were subject to the whims of the workers’ “patrones.” Some, like my parents, went through the torturous, expensive process of making our housekeeper legal. Most Texans just figured they were paying better than in Mexico, and providing a foothold in the United States was enough. For some newcomers, that was true: Their children went to public schools alongside the rest of us and grew into productive adults.