In the coming weeks, as Houston turns its attention to rebuilding areas devastated by Tropical Storm Harvey, people like Jay De Leon are likely to play an outsized role — if they stay around.

De Leon, 47, owns a small construction business in Houston, and he and his 10 employees do exactly the kind of demolition and refurbishment the city will need. But like a large number of construction workers in Texas, De Leon and most of his workers live in the United States illegally and that could make things complicated.

The Pew Research Center estimated last year that 28 percent of Texas's construction workforce is undocumented, while other studies have put the number as high as 50 percent. Construction employed 23 percent of working undocumented adults in Texas at the end of 2014, higher than any other sector, according to the Migration Policy Institute.