Say Engine Driven Pump (EDP) output low or zero. Most obvious reason seized engine core, so you’ve done a severe damage shutdown.
now the hydraulic system pressure is being maintained by the electric pump only. It has about 1/4 the flow rate of the EDP. So if you make a lot of hydraulic demands you may exceed the pump output at which point system pressure decreases. The onside accumulator will help a bit but the pressure could drop enough to triger the low pressure light (and the master caution and HYD on the system annunciator panel.
But this will be transient as the pump will catch up.
e.g. Single engine ops with a seized engine. Cycling gear and flaps simultaneously can give this condition for a few seconds. By the time you move your eyes to the panel it has usually gone out again.
So don’t sweat intermittent HYD when cycliing hydraulic services on one engine.
a windmilling engine is still turning the EDP and so this condition is less likely.
hope that covers it.