Steve Kraus writes:

I don't think a compressor failure or refrigerant leak will stop the
condensor fan (outside unit) from running although I suppose there
could be some with fancy electronics that tell it to shut down.

Plain old unfancy units have pressure switches that shut the unit down from
overpressure on the discharge side, underpressure on the suction side,
and/or overtemperature.

Look for a reset button on your compressor.