What happens to a dead star?

Answer 1

Technically a dead star is when a star no longer undergoes nuclear fusion.

Depending on the mass of the original star this will either be a white dwarf, neutron star or black hole. These are called stellar remnants.

Answer 2

It depends on the size of the star. The smaller stars shrink to become white dwarves and eventually black dwarves. The big stars collapse and either form a neutron star or a black hole. When big stars collapse, there's a massive explosion that people can occasionally see without telescopes.