What is the outcome of a star that runs out of hydrogen

Answer: The nucleus becomes entirely helium.

To shine, the stars transform their hydrogen into helium by means of nuclear fusion. When at half of its life a star is without hydrogen, the nucleus becomes entirely helium and the star declines, becoming colder and brighter due to the energy generated by the nuclear reactions, then the star begins to contract.

Nevertheless, if the star is bigger, this helium will be also consumed and the nucleus transformed in Carbon, then in Oxigen, and so on. Being the last transformation Iron until the star delivers all its energy.

Note this process will depend on how massive the star is.