A law slated to go into effect on Jan. 1 is designed to clamp down on Russian citizens and companies that the Kremlin thinks are avoiding taxes through the use of offshore tax shelters. The law requires Russians to disclose ownership of foreign assets and imposes a tax on them, part of something officials have referred to as "deoffshorization."
Experts point out that President Vladimir Putin wants to limit capital outflows in the face of economic and political troubles. Internationally priced Brent crude is near a five-year low, and the Russian ruble on Monday suffered its worst one-day drop since 1998.
Crude petroleum accounts for 39 percent of Russian exports, and refined petroleum 15 percent, according to data aggregated by the Observatory of Economic Complexity at the Massachusetts Institute of Technology.
Even before oil's declines, Russia's economy was suffering in the face of sanctions imposed by the European Union and the United States, and trying to absorb the domestic costs involved in annexing Crimea from Ukraine.
"With the Kremlin's concerns (about) finances, foreign intervention in Russia and dissenting social groups, this latest anti-corruption campaign is designed to shape the Kremlin's control over each, as the Kremlin faces a series of crises all at once," said Lauren Goodrich, senior Eurasia analyst at research firm Stratfor.
The Kremlin has a history of using anti-corruption campaigns to shape the finances of various groups, Goodrich said. Russia engaged in an anti-corruption campaign in 2003 that brought down a number of its powerful oligarchs, and it targeted some Russians with foreign ties in 2013.
Russian capital flight is expected to surpass $100 billion this year, and foreign investment in Russia has fallen by 50 percent in 2014 from the year prior, according to statements from Russia's economy ministry.
Marlen Kruzhkov, a Ukrainian-American attorney who represents investors from the former Soviet Union who want to bring money into the United States, said that many of his clients are concerned about the new law.
He expects some people to simply ignore it and risk violating the law with the belief that Russia has neither the resources nor the international heft to monitor properly and enforce it. But he said that many people will look for ways to take themselves out of the reach of the law by adding third-party straw men to hold their interests.
"Obviously, this is risky, as it creates the opportunity for such unrelated third parties to potentially lay claim to and exercise control over your interests, but many people will decide that this is the less risky course rather than compliance," he said.
Edward Mermelstein, a New York-based attorney for Rheem, Bell & Mermelstein who manages investments and other issues for Russian clients, told CNBC that depending on who is in charge of the legal process there, the law "can be used to either bury someone or show that the country is turning itself around and is not the corrupt state that it is being perceived as."
Mermelstein told CNBC that anyone who has a significant amount of holdings outside of Russia should be concerned.
"You all of a sudden show that you have companies and real estate outside of Russia, and the next question becomes where did that money come from?" he said. "It opens up a Pandora's box of who the government wants to target, so there's a potential to see more arrests."
Mermelstein said that Russia has a long history of setting up structures where businesses do as they please while the government looks the other way. He predicted that will change, however, with the new law.