One possibility for Trevor’s whereabouts had emerged late Thursday: A Greyhound bus had been stranded for hours on flooded Interstate 10, and those inside were on the way to the shelter. But it turned out to be a false lead. Trevor was not on the bus.

Still at the shelter, Ms. Kinsey said in a text message on Friday that her son remained missing.

Rod Carroll, the chief of police in Vidor, Tex., outside Beaumont, was still orchestrating water rescues on Friday from the police station where he had been posted for nearly 36 hours.

Since early Thursday morning, his employees had helped rescue dozens of people in the city of 10,000, and he estimated that a few hundred homes in the area had flooded. His was one of them.

Chief Carroll had been monitoring the radio from bed overnight on Thursday when he heard reports of severe flooding and people trapped in cars. When he got up to report for duty at about 1:30 a.m., he saw that water had started trickling in downstairs. He and his wife hustled to grab photos of their children and knickknacks from his wife’s parents, but soon the first floor was covered in a foot and a half of water.

“It came in like a wall,” he said.

They had been through this before, during Harvey, and Chief Carroll estimated it would again take them about 14 months to rebuild.