The gas gauge is just an indicator and each vehicle is going to be different. I know the older Datsun Z cars had two gas gauges, one was the main one which showed the volume of gas down to 1/4 tank, while the secondary one showed from 1/4 down to empty. The secondary gas gauge was very accurate to give the driver a true indication of how much fuel was in the tank. With today's gas gauges, like I said, it's just an indicator. You as the driver need to be aware of how much fuel is left in the vehicle and understand when you need to put more fuel in. This is a practical knowledge which comes from experience. Just because the fuel gauge is pointed at "E" does not mean the fuel tank is empty, just that the quantity is getting very low.
Even vehicle with a "Distance to Empty" reading are not that accurate. You have to know, when you are below a certain threshold, there isn't much fuel left and you need to start looking for a filling station.
A vehicle cannot run without fuel. When someone says "it's running on fumes", this is just a saying. They are just stating there is very little fuel left in the tank. A vehicle cannot run on fumes. If there isn't any liquid gas in the tank (compressed natural gas - CNG - excluded), the fuel pump cannot create fuel pressure which is needed to run the engine. Fuel injected vehicles are very dependent upon the fuel pressure being correct in order to inject the correct amount of fuel per injection cycle.