So far as running out of fuel being harmful to the injector-pump, it can't be good for it; but, then again, it won't kill it either.
The vast quantity of fuel that cycles through the return-line system ( about ten gallons for every gallon burned ) does so to COOL and LUBRICATE the injector-pump.
That being said, whenever the engine starves enough for fuel to "run out of fuel", the injector-pump will still be nearly full of fuel; the intrusion of air just causes it to "lose prime" and not be able to acheive a high enough pressure to pop the injectors.
Cranking the engine with the starter does not develop enough engine speed, nor is it of long enough duration to generate any heat, so the fuel remaining within the pump should be sufficient to keep it lubed until the engine fires.
That being said, running out of fuel in a busy intersection, or in the middle of a long bridge, can get you run over and killed.
Running out of fuel while pulling a big goose-neck full of cattle up a steep hill will result in the truck/trailer sliding backwards down the hill until it either jack-knifes or you are fortunate enough to manage to jam the corner of the trailer into the road-bank, and not go over the cliff on the other side.