Can a long pipe stop the flow of a liquid from a pump? If a pump is discharging a fluid into a pipe, is it possible to add a long enough pipe such that the flow of the liquid will be stopped and none will come out of the open end of the pipe?  
 A: When the liquid flows through a pipe, whether it is discharged from a pump or not, it's pressure changes. If the liquid flows in a horizontal pipe, upwards in a vertical or inclined pipe - the pressure will definitely drop. If it flows downwards, whether the pressure will rise or drop, it depends on the ratio of the friction, momentum and gravity terms in the pressure drop equation. Usually it will rise.
So, when Your liquid flows downwards, there is no chance for stopping the flow with a long enough pipe.
When Your liquid flows in a horizontal pipe, there is also no such possibility. The best You can achieve is to decrease the pressure to the saturation line when Your liquid will start boiling, this is called cavitation and usually should be avoided. Anyway, after Your liquid completely evaporates, it will further flow in the pipe and the pressure will further drop. If the pump continuingly supplies the pipe with fresh liquid, it will drive the mass flow in the pipe. 
When Your pipe is vertical and the liquid column pressure is greater than the pump head, You will experience so-called back flow that (if big enough) can do some damage to Your pump. Then the flow will probably stop.
A: The simple answers are:
1, if it is a centrifugal pump, the point where the pumps' characteristic curve is at shut-off head is also the point where there is no flow from the pump. You don't need an infinite long discharge pipe. Just need it long enough to create a back pressure equal to the pump's shut-off head.
2, If the pump is a positive displacement pump, the pump will attempt to create the pressure so that flow will occur. If flow stops, the pump will continue to move the liquid (pressure buildup) until something breaks.
