“The reserve funds have been something sacred. Putin always refers to them when he talks about economic difficulties,” Mr. Milov said. “They have been used as a strong, public indicator that the state still has capabilities.”

But they are shrinking fast with no economic revival in sight. Two sovereign funds, the Reserve Fund and the National Wealth Fund, are now down to less than $104 billion, compared with a combined $160 billion at the beginning of 2015, according to the Finance Ministry’s website.

The financial reserves are expected to run out by the end of 2017, just as Mr. Putin faces a campaign for a fourth term in the spring of 2018.

The Rosneft stash would help tide over the country for a longer period while the Kremlin ties its hopes to a rebound in the price of oil and the possible lifting of Western sanctions imposed over Russia’s annexation of Crimea and the Ukraine crisis. Prospects for the latter brightened with President-elect Donald J. Trump’s criticism of the American policy of isolating Russia.

For now, the Russian economy hovers around zero growth, and consumers still struggle with inflation caused by a sharp drop in the ruble, along with food restrictions imposed in response to the Western sanctions.

With minimal outside investment, Russia’s economic fate is increasingly in the hands of the state. New statistics from the federal antimonopoly service show that the government controls about 70 percent of the economy, compared with 35 percent in 2005.

Olga V. Kryshtanovskaya, a leading sociologist who studies the Russian elite, said the Ulyukayev case cast a shadow over the entire government. “People resent the fact that they had to give up French cheese in order to support the president’s policies and such corruption cases still erupt,” she said in an interview.