What happens to a diode when it break-downs?
At reverse breakdown voltage on a PN junction diode, you get a large increase in reverse current (normally close to zero) for a small further increase in voltage.

Breakdown is non destructive - provided thermal effects do not destroy the diode. Zener diodes are devices with specified low breakdown voltages that exploit this effect.

So for example a 10V 1W Zener could take 0.1A in reverse breakdown current continuously. If you exceed this thermal rating then the diode will be damaged in an unpredictable way.