Have a look at the zener diode characteristic (pictures below) ..
Once you pass the Pmax point, and this can be easily done by trying to apply to high voltage, the zener diode will be killed ..
Zener diodes are usually rated for 0.5W, 1W ,...5W, ..
For example, at 5.1V and 0.5W the maximum zener current is Imax≈98mA.
Your task is to make sure that with or without load the zener current is always smaller than Imax ..
In other words, don't apply a voltage directly to a zener diode; use serial resistor which will limit maximum current below Imax ..
Regards,
IanP