In the same way there was a nebula of gas and dust before the star was born, a new nebula is created from the explosion. Without an atmosphere, without all of the flames, stars really aren't that much. A little ball of heavy elements is left where the enormous star once was. This is the final phase of the star's life. The core of the star is left, some fires still burn, but there is very little fuel left.
Astronomers can see the dwarf after the nebula has dissipated.
Sadly, the White Dwarf eventually goes out. The life of a star is not always finished with the white dwarf. Sometimes the star continues to contract and its gravity increases. Imagine that the Earth contracted. First to half its size, then a quarter.