One oil rig was idle for weeks because a single piece of equipment was missing. Another was attacked by armed gangs who made off with all they could carry. Many oil workers say they are paid so little that they barely eat and have to keep watch over one another in case they faint while high up on the rigs.

Venezuela’s petroleum industry, whose vast revenues once fueled the country’s Socialist-inspired revolution, underwriting everything from housing to education, is spiraling into disarray.

To add insult to injury, the Venezuelan government has been forced to turn to its nemesis, the United States, for help.

“You call them the empire,” said Luis Centeno, a union leader for the oil workers, referring to what government officials call the United States, “and yet you’re buying their oil.”

The declining oil industry is perhaps the most urgent chapter of Venezuela’s economic crisis. Oil accounts for half of the Venezuelan government’s revenues, what former President Hugo Chávez once called an “instrument of national development.” The state oil company poured its profits, more than $250 billion in all from 2001 to 2015, into the country’s social programs, including food imports.

But those profits have evaporated with mismanagement and the drop in global oil prices over the past two years. Now, even Venezuela’s subsidized oil shipments to its vital ally Cuba are slowly being phased out, oil executives with operations in Venezuela contend, forcing Havana to look to Russia for cheap oil.

For Mr. Chávez and his handpicked successor, President Nicolás Maduro, Venezuela’s oil wealth has been essential to the nation’s identity and sovereignty, the financial might behind its regional ambitions and its angry defiance of the United States.

The United States has always been a huge market for Venezuela’s oil. But with Venezuela’s state oil company hobbling along, it was actually forced to start importing oil from the United States.

Early this year, the United States began shipping more than 50,000 barrels a day of the light crude that Venezuela needs to prepare its own oil for export, joining a handful of suppliers that have become vital to keeping the country’s oil industry afloat.

Even that lifeline is tenuous. Venezuela’s state oil company, PDVSA, is struggling to pay for the foreign oil. Some tankers wait in port for as long as two weeks to be paid, and sometimes they leave because of a lack of payment, said an oil executive who requested anonymity to avoid reprisals from the government.

The problems are just some of the reasons Venezuela’s oil production has plummeted to 2.4 million barrels a day, down 350,000 barrels from a year ago. That is nearly a million barrels below what it was in 1998 when Mr. Chávez took power.

Venezuela is racked by shortages of foods like corn and rice, which it once easily imported using the company’s vast foreign currency revenues. Essential medicines like antibiotics have disappeared. The economy is set to contract by 10 percent by the end of the year and has already seen triple-digit inflation.

The price of bread alone has doubled from month to month, now about 50 cents a loaf in many places, at a time when the oil workers here say they are making less than a dollar a day because of the inflation.

“We are practically working for free,” said Pedro Velásquez, a supervisor at an oil field in the town of Punta de Mata.

Whatever money the government can muster to improvise patchwork repairs in its oil fields and processing plants is now drying up.

With the state oil company hobbled by debts, two-thirds of its exports go to paying off Chinese and other lenders. The company is running out of resources to pay international technicians, or even its own people.

“The decline is speeding up, and that will continue to happen,” said Lisa Viscidi, a Latin America energy expert at the Inter-American Dialogue, a Washington research institute. “Conditions are getting worse and worse; there’s less and less money to invest.”

The condition of Venezuela’s state oil company has international oil traders concerned that its collapse could jolt an otherwise oversupplied global market. They note that when labor strife brought nearly all production in Venezuela to a halt for several weeks at the end of 2002 and in early 2003, global prices jumped more than 30 percent, marking the first in a series of international crises that ushered in a decade of climbing oil prices.

Venezuela accounts for less of the international oil market today, but its exports still make up roughly 2 percent of the world’s output. That means that a serious decline in Venezuelan exports, especially if accompanied by a crisis in Nigeria or Iraq, could tighten the market enough to send oil prices climbing again.

“A collapse in Venezuela would be an accelerator for oil prices; it would be a total shock,” said Helima Croft, the chief commodity strategist for Royal Bank of Canada. “This country is literally imploding.”

Right now, she added, “There is no oil producer that is falling apart as fast as or as dramatically as Venezuela.”

Neither PDVSA nor its American subsidiary Citgo agreed to requests for interviews.

The challenges ahead are ever-present here in the vast oil fields of El Furrial, in northeastern Venezuela. Beneath the flat, grassy expanses lies the very grade of oil that Venezuela must now import to blend with its large reserves of heavy oil to ship them abroad.

At its peak, El Furrial alone produced 453,000 barrels a day, equivalent to about 80 percent of the national production of Ecuador. But in 2009, Mr. Chávez nationalized Wilpro, an American consortium that handled the complex natural gas injection at the site designed to coax more oil out of the ground. Production has declined by more than half.

Workers at El Furrial today tell a story of decline and mismanagement. There is not even enough drilling mud — the most basic fluid required to keep drill bits cool and well bores clear — to keep all of the rigs running.

At one PDVSA well pad here, China National Petroleum Corporation now fills the gap left by Wilpro. But the site had not been operating for several weeks because PDVSA had not delivered a vital piece of equipment that suspends tubing over the well.

Once completed, the well might produce 3,500 barrels of oil per day, but it was not clear when that would be.

“It’s the first time we’ve ever gone three weeks waiting this way,” said Nelson Ruiz, a manager. “Normally we would get the project going after one signature, and the drill would be in the ground.”

But it is the issue of food that is demoralizing the workers the most.

Workers at one production site described how they eat so little food now, they watch out for their co-workers in case they faint. Claudio Lezama, who has spent the past eight years at the site, said he weighed about 200 pounds several years ago. Between his manual labor and being able to afford only one meal a day, he is now 145 pounds.

Sitting in a trailer where workers take their breaks, he said that he worked as a stone mason to afford to feed himself during his time off. A colleague said she had taken to reselling food like yucca, cheese and eggs.

“You’re a black-market seller,” said Mr. Lezama, chiding her for raising prices when food was in short supply in Venezuela.

In a complaint filed in July by a group of workers at the state oil company, the workers detailed a history of extensive petroleum leaks since 2012 in El Furrial stemming from lack of maintenance and costly infrastructure that was left abandoned.

The complaint said the problems also posed a health risk for surrounding communities.

“All this has been hidden from view, generating multimillion-dollar losses,” the complaint said. “We workers are extremely angry because no one has done anything to put a stop to this disaster.”

These days, some oil workers fear that simply going to work puts them at risk. Carlos Robles, a union leader, spent a recent afternoon talking to supervisors of a well about a number of attacks by armed gangs who robbed that facility and others of laptops, air-conditioning units and metal equipment.

It was getting to be 6 p.m., the time that workers warned that the gangs begin to prowl and the streets of El Furrial were empty, looking as if a curfew were in place.

“The only thing between us and being robbed is God and the Virgin,” said Juan Díaz, a supervisor at the site, as his shift continued into the night.

International service companies like Halliburton and Schlumberger are scaling back their operations as Venezuela’s state oil company struggles to pay its debts to them — as much as $25 billion — with a flurry of bonds and promissory notes. And as the production from El Furrial and other fields plummets, the state oil company has to lean ever more heavily on Citgo, which is being forced to leverage to the hilt.

Last year, Citgo borrowed $2.5 billion to keep PDVSA afloat. And now it plans to borrow an additional $800 million to update a refinery on the island of Aruba to produce synthetic light oil, according to executives who have been briefed on the plans.

Mr. Centeno, the union leader, said Venezuela’s state oil company had become so strapped that it had stopped providing its workers with new boots, helmets and gloves.

“PDVSA is on the floor now,” he said.