HOUSTON — For six months, Sue and Roger Powell have been hoping to find a buyer for their 7,100-square-foot home in the Houston suburb of Katy. A week ago, after they waded out of it with a few suitcases on air mattresses, those hopes had largely faded. Then they got an unexpected call from their real estate agent: a house hunter was interested.

“Somebody actually called her before we got back in here,” Sue Powell said as she stood in her driveway last week, a safety mask around her neck and a pile of her possessions on the curb.

“I was really surprised,” said her husband, describing how they had “gondoliered” their way back home over Labor Day weekend. “I didn’t think anyone would be interested for years.”

But interest is rarely lacking here. The Houston metropolitan area grows by about 400 people a day and builds 40,000 housing units a year, making it the nation’s largest new-housing market, with 7 percent of residential construction. With light regulation and a civic model tied to growth, it has kept housing prices low by building everywhere and anywhere, and fast.

“You have a country that’s divided between high cost places like Bay Area and New York and higher unemployment areas like Detroit, and places like Houston pick up the slack,” said Issi Romem, chief economist at BuildZoom, a San Francisco company that helps homeowners find contractors.

And even after Hurricane Harvey revealed the city’s vulnerability to catastrophic flooding, leaving thousands displaced and still living in shelters, people here are betting that nothing can stop Houston’s continued growth.

Redfin, a national real estate brokerage firm, said its agents had 45 home buyers lined up to purchase homes here when the storm hit. Only eight buyers backed out because of the storm, and tour requests immediately rebounded a week later.

“I was shocked,” said Glenn Kelman, the company’s chief executive, who lives in Seattle.

For now, buyers and sellers are trying to figure out how prices have changed after the flood. The Powells’ potential buyer and many others are looking for a deal on a damaged home.

At the same time, many economists are forecasting that the price of undamaged homes will rise as demand outstrips supply. Early estimates suggest that tens of thousands of homes were damaged, and developers are worried about labor shortages as repairs get priority over new construction.

But as insurance and government money comes in, developers and real estate agents are betting that the area will quickly clear the backlog and continue along its normal trajectory of adding homes and people.

Throughout Houston proper and the surrounding suburbs, developers sprawl ever outward, paving over pastures and former wetlands and leaving nothing to absorb the water, when it comes.

“It is one of the most affordable housing markets in the country because people were able to build in places where they were likely to get flooded in the future,” said Svenja Gudell, chief economist at Zillow, the real estate data service.

Houstonians lose track of how many times they’ve been flooded. They repeatedly renovate or rebuild on elevated platforms and say they will go higher the next time if they have to.

Stefanie Asin and her husband, Jake Everett, live about a block from Brays Bayou in an area of Houston called Braes Heights, where the flood reached the middle of stop signs. After the storm they sat on their porch watching motorboats go by. Their closest neighbor was pulled from the roof of his house by a helicopter.

Their own home was fine because after the last flood, two years ago, they moved out and built a new one on an elevated platform, returning in March. The storm waters of Harvey rose up six of their seven front steps.

“We have stairs everywhere — front, back, garage,” Ms. Asin said. “We have stairs going into the backyard.”

Elevated homes are common in Houston, particularly around Ms. Asin’s neighborhood. In July, the City Council approved construction on the first nine homes in a batch of 42 near Brays Bayou that will be elevated using FEMA funding.

The appeal is particularly obvious right now: Elevated homes sit untouched above devastated houses with massive piles of debris all around them. Across the street from Ms. Asin, Arturo Loza, part of a Mormon volunteer relief effort, was helping gut a flooded house with a sink, cabinets and piles of books heaped in front.

“One word: wrecked,” he said.

Ms. Asin had been through three large floods since she moved near the bayou two decades ago. In Harvey, her losses were contained to the garage, which was not elevated, and so her daughters’ cars were ruined, and a refrigerator was left floating. But this was nothing new. She said her family had lost five cars to rain and water damage in the last three years.

Asked why they had bought a home in the neighborhood to begin with, Ms. Asin said: “The house was built in 1955 and it had never flooded. We thought, it hasn’t flooded yet!”

Then Tropical Storm Allison hit in 2001 and left a foot of water on the ground floor of the house. “We got it remodeled,” Ms. Asin said. “They told us it was a 500-year flood.”

But in 2015, the so-called Memorial Day flood almost completely covered their front yard, and Mr. Everett was photographed standing on a little patch of ground surrounded on all sides by water.

That flood left three inches of water in their home, enough that everything had to be torn out — Sheetrock, cabinets, floors.

They’d had enough, and considered moving away, but decided to stay put. “We were looking at how to come up with the mortgage for somewhere we didn’t really want to live versus building our dream house,” Mr. Everett said.

So they put up their dream house – seven feet above the street level.

A builder, Brian Silver of BAS Concepts, said that over the last 15 years, his company had built more than 50 homes around Brays Bayou that were elevated in some way – including Ms. Asin’s – and 10 just in the last year.

“If you elevate your house, you’re out of the floodplain,” Mr. Silver said, adding that it was his practice to build new homes a foot above the elevation that FEMA expected floodwaters to rise or the high-water mark of the last storm — whichever was higher.

He predicted that after Harvey, even more homeowners would decide to demolish their flooded homes and build from scratch, but higher, and that already elevated homes would increase in value. (According to the Insurance Information Institute, homeowners in flood-prone areas are often required to elevate their houses to get flood insurance, and the areas designated can change with storms and development.)

In the meantime, even as National Guard trucks remained on the streets and drones assessed damage, the steady stream of migration continued.

After the hurricane, when the city was still underwater in some places, Christine Garcia and her boyfriend, John Klein, packed their car in Chicago and set off on a long-planned move to Houston. They were not entirely sure whether their apartment would be habitable, and were unable to get any answers from their landlord, but they arrived to find their two-bedroom duplex was dry.

The couple is renting now, but they moved there because they would like to buy eventually. Mr. Klein was attracted by the area’s cheap housing – he said he had seen homes advertised for $50,000 – though he quickly came to appreciate the risks that such a low price entails.

“I’m sure you’d pay as much in flood insurance,” he said, with perhaps a bit of hyperbole, “but it’s almost worth it.”