What is the type of nozzle used on the MiG-21 and MiG-27?
Mig-21F, the first version of Mig-21 to be called as such, used a Tumansky R-11F-300 engine, which had a (variable) convergent nozzle. Later versions used Tumansky R-13-300, which was similar to the R-11 and Tumansky R-25-300 which had variable convergent nozzles as well. The Mig-27 used the Tumansky R29B, which has a convergent-divergent nozzle according to the manufacturer's site.

In theory, the aircraft speed is not limited by the exit speed, but the extra speed imparted to a mass of air by the engine (more the $\Delta v$, more the thrust). Basically, there is nothing that prevents an aircraft with convergent nozzle from attaining supersonic speeds, albeit the system is very ineffecient.


If the designer is ready to accept a weight and fuel consumption penalty, he/she can use a supersonic convergent nozzle. Though this is ineffecient, for short duration, this would be acceptable.
Another point to note is that the high exit temperatures means that the sonic velocities in the exhaust are nuch higher than the freestream ones. This means that the difference in speed is there, though the mach number may be less.