  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. In particular,
we prove that the approximations used to evaluate the axion emissivity in red
giants agree with the exact result within $10\%$, comparable with other
uncertainties in these studies. In addition, this prescription allows the red
giant and white dwarf bounds to be extended to massive axions.
