It will continue to do so until it reaches the temperature where He fusion becomes possible. Something else has happened to the core region though before it reaches this temperature. Electron degeneracy is a state of matter. Other states of matter that you are familiar with are, solid, liquid, and gas. The difference in these states is in the way that individual particles in the material interact.
Solids are, well, solid.
They have a rigid shape and a fixed volume. This is due to the strong interaction between the particles of the solid. Gases behave differently as we have seen. They have neither a fixed shape or volume. This is due to the lack of inter-particle forces.