But because the Helium core is degenerate, its size remains the same, so its temperature increases catastrophically. With a rapidly increasing temperature, Helium fusion takes off at a feverish pace, producing a dramatic surge in energy called the Helium Flash, in which a large fraction of the Helium is almost instantly fused into Carbon. The energy released in the Helium Flash finally overcomes the electron degeneracy, and the inner core can finally expand and reduce its temperature. The star has finally stabilized. The inert Carbon core is shrinking on itself, but it will never have enough mass to reach the 600 million K temperatures needed to begin Carbon fusion.
Helium fusion ceases for lack of fuel.
All fusion ceases, and the star is officially dead. This nugget of very hot Carbon, surrounded by a thin skin of Helium and sometimes a thinner skin of Hydrogen on top of that, is now a White Dwarf. The White Dwarf is beginning to cool and its luminosity is fading. It may take more than another 20 BY for it to cool into darkness. The Planetary Nebula has expanded so far away from the White Dwarf that it is finally too thin and cool to glow, and this debris now becomes part of the Interstellar Medium, available for building another star someday.