What Happens To A Star When It Runs Out Of Hydrogen?

It expands into a red giant, and depending on it's size it either blows away all it's outer layers and leaves a white dwarf, it explodes and leaves a planetary nebula, or it explodes massively and leaves behind a black hole.

Stars are born from clouds of gas and then they enter a stable period of about 5 billion years. Their brightness is due to fusion reactions fuelled by hydrogen. As a star's supply of hydrogen runs out, the high radiation pressure produced by the fusion reactions decreases. Without this outwards pressure, the force of gravity causes the star's core to contract. This increases the temperature of the core, making it hotter than it was during the stable period. The core is now mainly helium. Eventually, the core temperature becomes high enough for further more complex nuclear fusion reactions to occur.

The new fusion reactions cause a higher outward radiation pressure than before. At this point the inward gravitational forces are unable to balance the radiation pressure and the star expands. It expands so much that the outer layers cool to about 3000 °C. Because the surface is cooler it looks red (only red-hot, not white-hot), so this type of star called a red giant. When our Sun reaches this stage it will be so large that the Earth will get burned inside it! But this won't happen for at least another 2 million years!

It implodes then explodes creating a supernova.

It becomes a neutron star or a black hole.

All left of it is a carbon core, it becomes a black dwarf.