Water Heater
While Poppa is correct, it actually takes quite a long time for that to happen. It would probably mean at least a day, probably longer. So the key is that if you are running on the water tank, you do need to shut off the water heater as soon as you discover that you are out of water. And you also need to turn it off if you shut off the city water when using it. But much more likely to cause you harm when your tank runs dry is the water pump. When there is no water in the tank, the pump will just run and run until it quits. The pumps will not be harmed by running out of water immediately either, but they will be damaged if allowed to run dry for hours. I got to replace mine shortly after we got our new motorhome from such a case.