BROWNSVILLE, Texas >> Homar Veloz lives in South Texas, but on the wrong side of the border wall — separated from the rest of the United States by a long line of vertical steel bars standing up to 18 feet high.

His house on the 1600 block of Milpa Verde is located in an odd swath of Brownsville, Texas, that runs between the border wall and the Rio Grande — a netherworld that is officially still America but which somehow got left on the Mexican side of the wall.

Visitors often get confused, including Veloz’s daughter, who was nervous the first time she visited the house, and reminded him that she hadn’t brought her passport.

“She said, ‘Dad, don’t tell me we’re in Mexico,’” he recalled. “Because she’d gone past the fence.”

One of his neighbors made a homemade billboard that she posted at the end of her driveway to make things clear: “We’re Part of America.”

On long stretches of the Southwest border, a clearly visible boundary separates the United States and Mexico. In parts of Southern California and in the Arizona desert, it takes the shape of a wall running right along the line, with one country on each side.

But in South Texas, things get fuzzy. The border there, by tradition and international treaty, is the Rio Grande, and no one has yet figured out how to build a border wall in the middle of a river. As a result, the fence that elsewhere would trace the southern edge of the United States can run, as it does in Veloz’s neighborhood, more than a mile north of the river.

That has created an oddly isolated zone of homes, ranchland, industrial sites and nature preserves that locals call a no man’s land, between the barrier and the border — a place that dozens of Texans call home.

President Donald Trump’s border security plans call for miles of new border fencing in South Texas, much of it in the Rio Grande Valley, which has emerged as a key corridor for unauthorized migration into the United States. The border wall proposal has raised questions about cost and effectiveness across the country, but one of the biggest issues here in Texas is the way the plan would significantly add to the buffer zone, a bizarre region that has amused, angered and isolated the people who live and work there.

“It was a bunch of yo-yos up in D.C.,” said Cuban A. Monsees Jr., 71, who lives north of the fence, not far from Veloz, but owns more than 4 acres on the south side. “It should be closer to the river, No. 1,” Monsees said of the fence. “Where it should have been was within 150 feet of the river bank, rather than, in some cases, a mile and a half away.”

This netherworld between the end of Mexico and the visible beginning of the United States is a subtly off-kilter place unlike any other in America.

Residents, property owners and ranch hands in South Texas gain access through dozens of openings and gates, in many cases by punching in secret access codes on a keypad. One household south of the fence in Brownsville put its mailbox on the north side, presumably to make life easier for the letter carrier.

The pace is slow, the property cheap: Veloz rents his house for $350 a month. Another resident doesn’t have a mailbox because the mail never comes, and burns his trash because the refuse collector never shows up.

The fencing that created the netherworld went up during the George W. Bush administration, but limitations on where the fence could be constructed are much older.

A treaty signed by the United States and Mexico in 1970, and later ratified under President Richard Nixon, to resolve some boundary disputes also prohibits construction of anything that would obstruct the normal flow of the Rio Grande. It applies not only to the river’s main channel, but also adjacent lands, hence the decision to keep the fencing well clear of the river.

The fencing was intended to help keep out drug smugglers and unauthorized migrants. But in some ways it has complicated the Trump administration’s attempts to halt the waves of migrant families from Central America who have been crossing the border recently. Those who cross in the Rio Grande Valley do not have to breach a border wall to claim asylum, because they reach U.S. soil and gain that right as soon as they have crossed the river. So for them, the situation is no different than it would be if there were no wall or fence at all.

A number of legal battles have broken out between the Trump administration and property owners along the river, over the government’s plans for additional barriers north of the river that would cut off and fragment ranches, nature centers and historical landmarks.

Life on the south side of the Bush-era fence has been difficult for the nonprofit Nature Conservancy. It owns the Southmost Preserve near Brownsville, a nesting habitat for rare birds and the site of one of the last two large stands of native sabal palm trees in the country. Most of the preserve — 831 of its 1,014 acres — is south of the fence.

At one time, a preserve manager lived in a house on the site, and many donors and researchers visited or even stayed overnight. But after the wall was built in 2009, slicing through the preserve, the live-in manager was moved out for safety reasons, and visits by donors and researchers dwindled. There have also been negative ecological impacts, including disruptions to the free movement of ocelots, an endangered species.

The federal government initially offered the Nature Conservancy roughly $100,000 for a right of way through the preserve, but the group sued and was awarded nearly $1 million — less than one-third of the $3.1 million it spent to purchase the preserve.

“Visitation in general is not what it was,” said Laura Huffman, the Nature Conservancy’s state director. “It’s changed the story about the preserve. One hundred percent of the time now the conversation about Southmost Preserve is not about sabal palms and habitat protection for the ocelot. It’s about a border wall, and that’s not our conservation work.”

In some ways, this region is not unlike other rural parts of Texas. There are vast, carefully maintained fields of corn and sugar cane, horse stalls, dirt roads, power lines and tail-swishing cattle. There are radio towers and quaint ponds and houses with swimming pools and unleashed dogs chasing passing vehicles.

Brownsville officials say Veloz and his neighbors on Milpa Verde are provided the same municipal services as any other residents.

“Our response times are not affected,” said Jarrett Sheldon, chief of the Brownsville Fire Department. “People on the other side of the wall, they’re going to get the same response.”

Residents south of the fence don’t need to rely solely on Brownsville emergency responders for their security, in any case: They live in one of the most heavily patrolled communities in the country. Border Patrol agents come through regularly in vehicles and helicopters, along with sheriff’s deputies, constables and state troopers. Cameras are mounted high atop the fence, many of them aimed at the openings and gates, and residents have long grown accustomed to being photographed and filmed as they travel to and from their homes.

Veloz said it all makes him feel safer. Migrants and smugglers are a common sight. Years ago, he said, people used to knock on his door at night. “I wouldn’t answer,” he said, “because I don’t know what their intentions are.”

Being Texans, though, many of the people who live between the fence and the river say they don’t count exclusively on the government to keep them safe. One recent afternoon, a retired refrigerator repairman wearing camouflage clothing strolled south of the wall with a handgun in a holster on his hip. Monsees was even more heavily armed as he spoke outside his home while sitting in his pickup truck.

“This is a single-shot .410, and that’s a single-shot .22, and I keep the pistol between the seats,” he said.

In another buffer-zone community along the river about 50 miles northwest of Brownsville, on a muddy dirt road outside the town of Donna, Arturo Munoz, 72, sat in the carport of his house just south of the border fence, sipping a Bud Light. His dog Max lay at his feet.

“It’s just about the same as on the north side,” said Munoz, a retired welder and Vietnam veteran, though he conceded that he has no mail service, no landline telephone and no cable television.

He said he bought the property nearly 15 years ago because he grew up nearby and feels a connection to the area. When it came time to build the border fence, he said, the government made him an offer he could refuse, and he did. He stayed put, and the wall went up just north of his white-brick home, right behind a line of trees in his backyard.

“It’s a lot safer than in town,” he said. “I lived in town. I was renting, and got broke into three times.”

He described riding his bicycle near his house one day and seeing a few migrants walking along. He said he waved to them and pedaled on. They had crossed the river on their journey to America, and had found it. Sort of.

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