Fire hydrants don't ever run out of water since fire hydrants are connected to the public water supply.
As long as the public water supply such as the water tower and the well or water source the water is coming from has plenty of water then the fire hydrant will never run out of water.
Fire departments also keep a tanker truck full of water to be ready to begin fighting a fire and in case there's no water supply locally.
But when a fire truck is connected to a fire hydrant connected to the water supply the fire department has plenty of water to fight the fire.
However there are also some fire hydrants known as dry fire hydrants which are just a pipe that is buried in the ground and pulls water from a lake or other reservoir.
So if that lake or reservoir runs out of water then the fire hydrant would run out of water.
But water from fire hydrants that are in cities and towns have plenty of water under pressure being sent through them and the fire trucks pump increases the water pressure to help fight the fire.