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The diode is neither shorted nor open. It is a zener diode and it is conducting in both directions. If it were truly shorted, it would read closer to zero ohms in both directions.
It depends on how the diode is damaged. There are generally two cases. One, the diode is shorted, and conducts with a low impedance in both directions. The other, the diode is open, and does not conduct, having a high impedance, in both directions. The effect depends on the particular circuit. In a power supply, a shorted diode will often blow the fuse, while an open diode will result in no output, or in high ripple voltage output. Is it possible that diode has normal voltage output but wrong current,meaning low mA?
With a 10mA forward bias current, if the voltages at the anode and cathode of a diode in a circuit are found to be the same, then the diode most likely to be shorted.
There must be a break in the power supply elsewhere in the circuit. I suggest a blown fuse The only diode that generates electricity is a solar cell
Assuming the DMM is rated to test diodes (not all are), meaning that it presents more than forward drop voltage to the diode, a shorted diode will test nearly zero ohms, usually in both directions.