"Collapsing core" refers to a situation or process in which the central or main part of something weakens or fails, causing the entire thing to crumble or fall apart. Full definition
The system consists of a nebula and a neutron star, the incredibly dense collapsed core of the exploded star, still in the orbital embrace of its companion star. (sciencedaily.com)
A programme of fundamental NHS reform — on financing and ownership — could, paradoxically, convince the electorate of Labour's financial competence and play a crucial role in rebuilding Labour's fast collapsing core vote. (labour-uncut.co.uk)
Instead, the intensity of the X-rays coming from SN 2010da were consistent with a neutron star — the dense, collapsed core remnant of a supernovae. (sciencedaily.com)