= Solution
After its giant phases, the Sun ejects much of its envelope and leaves a carbon–oxygen <white dwarf>. The remnant mass lies below the <Chandrasekhar limit>. Its support is chiefly <electron degeneracy pressure>: the <Pauli exclusion principle> forces electrons into distinct momentum states even at low temperature, giving $P\propto\rho^{5/3}$ when they are nonrelativistic. Consequently pressure support need not cease when nuclear burning ends. The <white dwarf> subsequently cools and fades.
The process called inverse beta decay here is <electron capture>, $e^-+p\to n+\nu_e$, becomes possible for free particles when the electron's total energy exceeds approximately $(m_n-m_p)c^2\simeq2.6m_ec^2$, corresponding to a kinetic energy about $1.6m_ec^2$. Electron capture on nuclei has thresholds modified by nuclear binding energies. In a solar-mass progenitor's ordinary <white dwarf> remnant, the <Fermi energy> is below the relevant capture thresholds, so the electron population providing support is stable. At much higher density, electron capture can reduce the electron density and pressure and promote collapse; this is why stability against <electron capture> matters in assessing degeneracy support. \b[The Sun ends as a cooling white dwarf, rather than a neutron star.]
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