If you want to know what happens to "fakes" when they're recovered by the FBI or the U.S. Postal Service- the two federal law enforcement agencies that handle most cross-border counterfeit art frauds- click here.
The distortions that result from forgeries being traded in the market are twofold: (i) the historical record is distorted both directly and indirectly by potentially leading to the rejection of the most unusual (and often most informative) artworks for fear of inauthenticity and (ii) the market's price allocation mechanism is distorted by artificially inflating the supply of works by a given artist. These distortions combined with the fact that fakes are notorious for making their way back into the market make it pretty clear that what federal and state law enforcement agencies should do with a recovered fake is "shred it, incinerate it, [or] stamp it so that no one will be fooled again," as Catherine Begley, a former special agent in the New York office of the FBI, said. However, as the article rightly points out, this is not always possible as a result of judicial control over the destruction of counterfeit property (a court order is required) and the overlap between stolen works and fakes (the law generally requires that a stolen artwork, even if fake, be returned to its righful owner).