  The axion-electron coupling $g_{ae}$ is a generic feature of non-hadronic
axion models. This coupling may induce a variety of observable signatures,
particularly in astrophysical environments. Here, we revisit the calculation of
the axion-electron bremsstrahlung and provide a general formulation valid for a
non-relativistic plasma with any level of degeneracy and for any axion mass. We
apply our result to the Sun, red giant stars and white dwarfs. The most
relevant impact of the corrections is in the core of red giant stars, where we
find a reduction of $\sim25\%$ in the axion emissivity with respect to the
calculation in the completely degenerate approximation, showing the need for a
reliable prescription valid at intermediate degeneracy.
