Hi,
If a pump has a minimum flow control valve which is fail open and say for instance this valve fails (open) would it be over the top to also trip the pump ?
Selecting a pump and motor combination that will function under all system conditions is essential. It is typical to select a non-overloading motor. This usually means selecting a motor 20-30% larger than the power required at the design point. This means that one will pay a slight efficiency penalty for selecting a non-overloading motor and also a higher upfront cost. The operational problems and costs that are avoided, however, far offset the relatively minor upfront cost.
Most installations dont have such a feature - pump may run to end of curve but is not an immediate risk to machine integrity or plant safety. Long term operation at end of curve may cause impeller damage due to insufficient NPSH, so a low pressure alarm at DCS should do.
Am assuming you have motor overload-overcurrent protection when the pump goes to end of curve as discharge pressure collapses when this min flow CV fails open, hence no need for further instrumented trip protection.