I am learning about the lives and deaths of stars with a solar mass of 0.4-2. What I understand is that once the star stops hydrogen fusion after using up all its hydrogen, the star leaves the main sequence and starts becoming a red giant. The pressure of gravity causes the core to contract (no outwards pressure anymore because there is no more hydrogen fusion) and thus become hotter and hotter. At a certain point, the core stops contracting because the electrons are packed as densely as nature allows them to be (electron degeneracy).
At the same time, hydrogen fusion is taking place in the shell material of the star, dumping 'helium ash' on the core, which causes more mass to press upon the core, causing the core to contract even more. And that is my question: how can the core contract more after having reached electron degeneracy? I thought they could not be packed more closely?