There's no such thing as "exclusive rights" on a drug that's off patent.
Yeah, there is, in the U.S. at least. The FDA's Unapproved Drug Initiative
, among other things, grants pharmaceutical manufacturers the exclusive right to sell the drugs they test under the program. It's the reason that colchicine, which had been around for hundreds of years and was cheap and common prior to the program, is no longer available as a generic. Another screwed-up situation is that of albuterol, which was also cheap and widely available. In that case, mandated changes to the drug's delivery system to remove CFCs (even though using CFCs was otherwise legal in this application) allowed manufacturers to patent new delivery systems, and albuterol is no longer available as a generic even though the drug itself is not patented.
In both cases, it was administrative action by the FDA that was solely responsible for forcing drastically increased drug prices on people.