If you unplug the injectors it keeps running? You unplug all of the injectors at once? Do you also unplug the cold start?
If you unplug them they should stay closed and the engine should stall

They are possibly dirty as when they get crap in them they stay open a bit. Reason is the build up of crud stops them closing properly so a bit of fuel leaks past.
Get them cleaned and see what happens