The Buran orbiter was damaged during its test flight because of an issue with the heat management system, and I think the engineers had decided that it wouldn't fly again. The one that was supposed to take Cosmonauts up be fully complete and whatnot was named Ptitchkya, or 'Little bird'. Keep in mind that 'Buran' was just the name of that specific flying shuttle, kind of like 'Columbia', 'Challenger', 'Discovery', etc.
http://en.wikipedia.org/wiki/Ptichka_(spacecraft)
None of these shuttle will fly again, but if all the heavens came together and the grand vision of the soviet republics reborn was to Make It Happen, Ptitchka would be the one. It's still intact and owned by Kazakhstan, sitting in the MIK building at Baikonor.
