A battery is a good example of a
power supply which is not acting as a power supply. In this linked example, it is acting as a voltage regulator capping its parallel contribution to a circuit at the battery's rated voltage. This battery does not have to contribute any amperage, in the form of amp-hours, to power a circuit connected to this battery in series with the remainder of this circuit. It could, instead, be charged by this circuit (namely, topped off with a very weak charging current). This will insure the survival of this battery's charge for a very long time while insuring that this circuit can also be powered for a very long time on this battery's voltage, alone.