SOCHI, Russia -- The ski jump sits shrouded in mist, its coat of snow undisturbed by any athletes hurtling down the ramp to take off into the air.

A year ago, the jump bustled with activity at the Sochi Olympics as the world's best ski jumpers -- including women, for the first time -- competed for gold. But it made some unwanted history as well, becoming a stark symbol of how some of the plans for President Vladimir Putin's $51 billion Winter Games went terribly wrong.

The cost of the facility soared during construction from $40 million to nearly $300 million. The overrun embarrassed the Kremlin, which publicly shamed the businessman involved, and he fled the country in the face of a corruption investigation.

Russia had vowed to pay for what became the most expensive Olympics of all time by getting super-rich private investors to take the cost from the state. Instead, as the first anniversary of those games approaches, at least two of those oligarchs are quietly dumping their increasingly toxic assets on the state -- forcing Russian taxpayers to pick up the bill.

For the oligarchs, it's a way to recoup billions of dollars as they struggle in an economy battered by plunging oil prices and Western sanctions. For Putin's critics, it's evidence of the crony capitalism that shields Russia's rich and powerful businessmen from economic pain.

Two key investors have unloaded properties built for the Olympics at a combined cost of $3 billion, a spokesman to Russia's deputy prime minister confirmed to The Associated Press. The issue is a major headache for Putin, who needs to pay off the oligarchs to keep them happy, while preventing the murky deals from triggering a wave of popular unrest.

The risks for Putin are magnified as the country enters recession and its rainy-day funds dwindle, even as Russia prepares for staging yet another major international sports event: the 2018 World Cup.

In addition, other oligarchs may now be waiting for the right moment to demand their reward or compensation for coming to the government's rescue by taking on what became unprofitable Sochi projects.

"They don't have any good options here," Sam Greene, director of King's Russia Institute at King's College London, said of the Kremlin. "They either have to take the public hit, or they have to take the opposition of the oligarchs."

For now, Greene said it appears that Putin is opting for coddling the oligarchs.

"There seems to be something of an emerging understanding ... that the government will help the titans of the economy to maintain the liquidity they need to stay in business," he said. "In return for that, they remain quiet, they remain loyal, but they also maintain employment and they keep moving money through the economy."

The ski jump and nearby ski resort first became a notorious example of Sochi's excesses in 2013 when Putin visited the construction site and publicly dressed down officials for allowing the original owner, tycoon Akhmed Bilalov, to incur massive cost overruns: "Well done!" Putin burst out, his voice heavy with sarcasm. "You're doing a good job!"

Bilalov fled Russia days later, after prosecutors launched a corruption investigation into why the cost of the ski jump had ballooned from original estimates of 1.2 billion rubles to 8 billion (then worth nearly $300 million). His case has not yet reached court, and he remains in exile in an unknown country.

Sberbank, which is Russia's largest bank and is run by close Putin ally German Gref, stepped in to buy the ski jump and ski resort at the government's request. It took out a $1.7 billion loan to fund more than 70 per cent of the infrastructure project. Today, the project loses money and the bank remains saddled with the massive debt.

For Sberbank, the solution has been to obtain Kremlin authorization to swap its Olympic project, which cost nearly $2.7 billion at the time, for theuch the media centre -- similar to a large convention complex -- would fetch if sold on the market. But the key to the deal is t minutes.

Back in Sochi, a company called Basic Element, which is owned by billionaire Oleg Deripaska, is trying to sell seaside condos that housed the Olympic athletes. The company spent $1.4 billion building Olympic infrastructure, but is not among those seeking to unload their assets to the state. Instead, it is trying to restructure its loans with a state-owned bank while holding onto its investment.

Its deputy director general, Andrei Elinson, said the company "never considered these projects as some sort of charity or sponsorship."

"We believe that we have delivered what we were asked for. Now we want them (the government) to give us a simple return on our investment," Elinson told the AP.

The legacy of Sochi's busted budget is causing concern about Russia's ability to pull off the World Cup in three years, now that the ruble has lost more half of its value and the economy is struggling under the brunt of Western sanctions over the crisis in Ukraine and the collapse of the price of oil.

The soccer stadiums are only a tiny part of the overall construction for the World Cup. There are 11 host cities that will require new highways, airport expansions, train links, metro lines and giant hotels that are unlikely to be used again.

Unlike Sochi, the World Cup will largely be funded directly by the Kremlin, either through the federal budget or through state-owned companies, with only a few oligarchs in the mix.

The ruble's plunge also means the price of building materials will soar, causing the World Cup to far exceed its original budget of $20 billion.

As a way to battle galloping inflation, Sports Minister Vitaly Mutko said in January that Russia will be looking to simplify the design of the World Cup venues without compromising the requirements of soccer's governing body, FIFA. He also said the government would be looking to attract private donors, although he would not say who these might be.

In the Olympics, the government produced a detailed plan of infrastructure to be built -- from arenas to new sewage works. By contrast, it's unclear what projects will be commissioned for the World Cup, apart from the stadiums. Plans for the most expensive World Cup infrastructure -- rail lines estimated to be worth $14 billion at the time -- have been repeatedly revised and are likely to be reviewed further.

Despite such uncertainty, a recent opinion poll conducted in Russia by the AP and NORC Center for Public Affairs Research showed that half the respondents expect the World Cup to be good for the economy. The survey of 2,008 Russian adults was conducted between Nov. 22 and Dec. 7, 2014; it had a margin of error of plus or minus 2.4 percentage points.

And despite Sochi's problems, the poll also found that 51 per cent believe the Olympics were an economic boon.