That would be "Procyon". Since its mass is only about 1.5 times the mass of our Sun, I would expect it to become a white dwarf.
a dwarf star
A neutron star is already the remains of a massive star that has run out of fuel.
Neutron stars do not have fuel. A neutron star is a remnant of a star that has already died.
Such a star will first have a supernova explosion, due to instability in the nucleus. Then it will most likely turn into a black hole.
If the sun had 10 times its current mass, it would burn through its fuel faster and evolve into a red supergiant star. When it runs out of fuel, it may go through a supernova explosion, leaving behind a dense core called a neutron star or potentially collapsing into a black hole.
The death of a star occurs when its nuclear fusion processes can no longer sustain the outward pressure generated by the energy produced in its core. This can lead to the star collapsing under its own gravity, culminating in a supernova explosion or the formation of a white dwarf, neutron star, or black hole depending on its mass.
Usually the fact that the star runs out of fuel.
helium
When its original source of fuel has run out for instance our sun runs on hydrogen, after the depletion of the original fuel is gone the suns core condenses creating helium were the star expands to great measures were it gets to a size were its limited supply of helium runs out either collapsing into a black hole or a dwarf star
The core is necessary for a star's existence, it's the engine that keeps it from collapsing. When this engine runs out of fuel or its fuel vanishes, gravity overcomes and contracts the star until matter from the radiative zone is compressed enough to start fusing hydrogen again to counterbalance gravity.
they become super novas and explode
This will happen when the star starts to run out of hydrogen fuel.