You asked:

What happens to our sun once it runs out of fuel?

Marshall Brain answers:

Our sun is a giant fusion reactor floating in space. It is composed mostly of hydrogen and helium. In the sun’s core, hydrogen is fusing to form helium. Those fusion reactions produce the light and warmth that earth receives from the sun.

Right now the sun is about 70% hydrogen. Eventually, most of the hydrogen in the core will all be converted to helium, and the core’s fusion reactions will cease. Then what? Lacking the fusion reactions that inflate the core, the core will collapse due to gravity. At that point, the collapse creates a great deal of additional heat in the core. The outer layers of the sun still contain hydrogen, and the heat from the collapsed core is very high – high enough to start fusion reactions in these outer layers, and to sustain them at a rate much quicker than the reactions in the original core. Those rapid fusion reactions inflate the outer layers of the sun, and it will blow up into a red giant.

The bad news about the red giant phase is that the enlarged sun will be big enough to engulf planet earth. The good news is that this event is approximately 5 billion years away.