HONG KONG — As the Chinese economy stumbles, wealthy families are increasingly trying to move large sums of money out of the country, worried that the value of the currency will fall and their savings will be worth less.

To get around the country’s cash controls, individuals are asking friends or relatives to carry or transfer out $50,000 apiece, the annual legal limit in China. A group of 100 people can move $5 million overseas.

The practice is called Smurfing, named after the blue, mushroom-dwelling cartoon characters, and it is part of an exodus of capital that is casting doubt on China’s economic prospects and shaking global markets. Over the last year, companies and individuals have moved nearly $1 trillion from China.

Some methods are perfectly legal, like investing in real estate elsewhere, buying businesses overseas, and paying off debts owed in dollars. Others, like Smurfing, are more dubious, and in certain cases, outright illegal. Chinese customs officials caught a woman last year trying to leave the mainland with $250,000 strapped to her chest and thighs and hidden inside her shoes.

If the government cannot keep citizens from rushing to the financial exits, China’s outlook could darken. The swell of outflows is a destabilizing force in China’s slowing economy, threatening to undermine confidence and hurt a banking system struggling to deal with a decadelong lending binge.

The capital flight is already putting significant pressure on the country’s currency, the renminbi. The government is trying to prevent a free fall in the currency by stepping into the markets and tapping its huge cash hoard to shore up the renminbi. But a deep erosion of those reserves may set off further outflows and create turbulence in the markets.

China is also trying to put the brakes on outflows, by tightening its grip on the country’s links to the global financial system. The government, for example, just started to clamp down on people’s use of bank cards to buy overseas life insurance policies.

Such moves have trade-offs. The limits create concerns that the government is pulling back on reform efforts that China needs to keep growth humming in the decades to come. But the near-term pressure also requires serious attention, given the global shock waves.

“The currency has become a very near-term threat to financial stability,’’ said Charlene Chu, an economist at Autonomous Research.

Navigating such problems is fairly new for China.

For years, China soaked up much of the world’s investment money, as the economy grew at annual rates in the double digits. A largely closed financial system kept China’s own money corralled inside the country.

Now, with growth slowing, money is gushing out of the country. And the government has a looser grip on the spigot.

“Companies don’t want renminbi and individuals don’t want renminbi,’’ said Shaun Rein, the founder of the China Market Research Group.

The Chinese central bank is fighting the downward pressure by purchasing large sums of renminbi, selling dollars from its currency reserves to do so. China’s reserves sank to $3.23 trillion in January. A year and a half ago, they stood at $4 trillion.

And the renminbi still faces plenty of headwinds.

The government has been cutting interest rates to stimulate the economy, making it less attractive for savers to keep their money in the country. Corporate profits are shrinking because China has too many spare steel mills, car factories, and empty houses, leading investors to seek better returns elsewhere.

Ronald Wan, a Hong Kong money manager who is on the boards of numerous state-owned enterprises in mainland China, said that pessimism was becoming the consensus.

“Among the companies I have been in contact with,’’ he said, “all of them have the intention of moving money out of the country.’’

Companies and sophisticated investors have more freedom to send out money legally for big-ticket purchases and investments. Overseas and domestic companies, which maintain bank accounts in various currencies, can also shift their cash, as well as borrow based on which currency they think will fall in value.

But unofficial methods abound.

The government, though, is trying to cut off some routes.

Two years ago, the government gave permission for insurers to invest 15 percent of their assets overseas, up from 1.5 percent.

But China abruptly told insurers this winter to suspend many of their overseas plans, according to Hong Kong financiers.