Power Supply Under Voltage:
Some "DC to DC" PWM IC have input under voltage shutdown.
Example: input voltage = 12 to 24 volts. output voltage = 5 volts. The IC might have a function where it will not function until the input voltage reaches 11.5 volts.
Power Supply Open Circuit:
I don't know what you are thinking about. Maybe the wire breaks and there is no load. Some power supplies are not stable at zero load. Many power supplies have a 1 watt resistor on the output to give the supply some load.
Power Supply Over Current:
Many supplies will limit the output current.
Example: 5V 1A supply will first try to keep the voltage at 5 volts. If the current gets above 1 amp it will reduce the output voltage to reduce the current.
Example 2: Many PWM power supplies have a current limit on the big transistor (MOSFET). It does not limit the output current at 1A but limits the transistor current to save the silicon.
Power Supply DeSat:
Back in the days of power transistors (not MOSFETs) there was a function that tested to see if the transistor was working good. There is a case where the transistor is told to be on but the current is too high and the transistor starts to open up. (very bad) The IC might see this happening and stop the supply.
Hope this helps. You can find examples of these on the internet.