If you're the US Fish and Wildlife Service, you send it to the National Wildlife Property Repository in Colorado. In a warehouse near Denver confiscated illegal animal artifacts are stored and then . . .? This article describes some of the process but doesn't answer some questions. First, if it's illegal for private individuals or groups of them, to possess something like a stuffed tiger, how is it that a government agency has that right? Second, what is to be the ultimate disposition of these artifacts? Are they going to be stored until some later century? Is there some kind of a expiration date on holding the hide of a grizzly bear that was poached by some European industrialist? Aren't these tragic remnants of the Peaceable Kingdom something akin to the nuclear waste generated by some American power plants, waste that can't be disposed of in any real sense? It's a problem.
This article on the subject doesn't shed much light on what will happen when the last rhino horn is confiscated.