Zener and Common Diode in series
I googled "zener in series with diode across coil" and came up with this circuit: -



So, if the zener were shorted out what would happen when the transistor open circuits: The current that was formerly flowing into the BJT would flow through the diode and back to the top terminal of the coil. This is a common protection mechanism for relay coils. Without that protection the voltage at the collector would rise to hundreds of volts and punture the collector-base region and this would happen in microseconds.

Yes, the transistor would die but the relay would deactivate very, very quickly because it dissipates the stored magnetic energy very quickly. If, on the other hand, you use a diode (without the zener) the relay will deactivate in several (maybe tens of) milli seconds. It takes this long to deactivate the relay because the energy built up in the coil (i.e. it's magnetic field) isn't naturally converted to heat that quickly when using just a diode.

A diode drops ~0.7 volts and if the relay current is 30mA that's an intial power dissipation of only 21mW.

However, if the zener is added, it effectively makes the diode drop more voltage (say) 10V and the initial power dissipated is more like 300 mW. This means that the relay coil loses its stored energy more quickly and the circulating current in the coil (that keeps making magnetism that keeps the relay activated) is drowned much more quickly.

The upside is that the transistor collector only sees a voltage that is approximately Vcc + 11V and anyone designing this circuit will make sure that the transistor is rated for this slight excess.