While on the main sequence, a star is stable because there is a balance between its self-gravity trying to make the star collapse in on itself and the outward pressure of the gas heated by nuclear fusion trying to make it expand. When the core of a star runs out of fuel and nuclear fusion stops, what will happen to the star?

The Star will collapse.

Explanation:A star is an astronomical body that has the capability to illuminate itself through hydrogen fusion.

The fuel used by the star is made of the Hydrogen, and it is the main fuel that helps the star to remain in position and stabilised.

The Stars fuse Hydrogen atom into Helium in its core in a process called hydrogen fusion. Once the fuel is finished and fusion of hydrogen stopped it will cause the star to collapse, the star tries to sustain itself and remain stable through its self-gravity and the outward pressure of the gas heated by nuclear fusion trying to make it expand.