The reason it runs worse with fuel is because the injector is leaking fuel into the cylinder, that cylinder fires prematurely (long before TDC) causing the engine to run rougher and the piston to knock as it is actually trying to stop the piston, it also runs "rich" because the fuel being leaked into the cylinder is not being atomized as it would through a good injector that was reaching firing pressure so the large droplets of fuel do not burn well and are expelled through the exhaust.
That is how a diesel fuel injector (nozzle) fails, I have never seen one fail where it would not flow fuel, if that happened something would break is the IP has no "dead head" relief valve and something would have to give.