CARACAS, Venezuela — When President Trump slapped surprise oil sanctions on Venezuela aimed at toppling President Nicolás Maduro, exports plunged and banking froze as the effects hit harder and faster than expected.

But in recent days it has become clear that Venezuela’s state oil company, the main target of the sanctions as Mr. Maduro’s bankroller, has found a few ways to survive, with some Russian help.

Many in Venezuela fear that the sanctions imposed last week will push the already suffering nation of about 30 million people into an even greater humanitarian catastrophe.

“I’m not sure the U.S. has a Plan B if this doesn’t work in getting rid of Maduro,” said Francisco Rodríguez, a Venezuelan economist at Torino Capital, a brokerage firm. “I’m afraid that if these sanctions are implemented in their current form, we’re looking at starvation.”

Venezuelan oil exports to the United States, which provide the biggest source of cash for Mr. Maduro’s government, plummeted 40 percent last week. Customers suspended contracts, banks suspended Venezuelan accounts, and a dozen tankers filled with Venezuelan crude sat stranded across the Caribbean.

“We can’t charge, we can’t receive money. Our finances are paralyzed,” said Reinaldo Quintero, head of the Venezuelan Oil Chamber, an industry group that represents the country’s 500 biggest oil service companies. “There will be major collateral damage.”

But crucial help came from Venezuela’s biggest oil investor, Russia’s state-run Rosneft. The company said in a presentation this week that it would increase its output in Venezuela this year despite the sanctions, and that it remained committed to the country, throwing a lifeline to Mr. Maduro’s government.

Venezuela’s economy has already shrunk by about half since Mr. Maduro came to power in 2013, causing millions of people to flee the country or skip meals to survive.

Now the new American sanctions could cut Venezuela’s oil exports by two-thirds, to just $14 billion this year, and lead to a 26 percent reduction in the economy’s size, according to Mr. Rodríguez, the economist.

Mr. Trump said the oil sanctions were meant to punish Mr. Maduro for human rights violations and force him to cede power to Juan Guaidó, the opposition leader whom the United States and many other countries have recognized as the rightful Venezuelan president.

The sanctions announced by the Treasury Department on Jan. 28 banned United States companies and individuals from dealing with Venezuela’s state-run oil company, Petróleos de Venezuela, or Pdvsa, which provides about 90 percent of the country’s hard currency. The sanctions essentially shut Venezuelan oil out of the American market.

Mr. Maduro, accusing the United States of sponsoring a coup attempt, has vowed to remain in power.

Before the sanctions, his country imported about 120,000 barrels of oil and refined petroleum products a day from the United States. The Venezuelans blended the lighter American oil with their own thick crude oil so it could flow through pipelines to ports. The American shipments halted last week.