  The stellar initial mass function (IMF), which is often assumed to be
universal across unresolved stellar populations, has recently been suggested to
be "bottom-heavy" for massive ellipticals. In these galaxies, the prevalence of
gravity-sensitive absorption lines (e.g. Na I and Ca II) in their near-IR
spectra implies an excess of low-mass ($m <= 0.5$ $M_\odot$) stars over that
expected from a canonical IMF observed in low-mass ellipticals. A direct
extrapolation of such a bottom-heavy IMF to high stellar masses ($m >= 8$
$M_\odot$) would lead to a corresponding deficit of neutron stars and black
holes, and therefore of low-mass X-ray binaries (LMXBs), per unit near-IR
luminosity in these galaxies. Peacock et al. (2014) searched for evidence of
this trend and found that the observed number of LMXBs per unit $K$-band
luminosity ($N/L_K$) was nearly constant. We extend this work using new and
archival Chandra X-ray Observatory (Chandra) and Hubble Space Telescope (HST)
observations of seven low-mass ellipticals where $N/L_K$ is expected to be the
largest and compare these data with a variety of IMF models to test which are
consistent with the observed $N/L_K$. We reproduce the result of Peacock et al.
(2014), strengthening the constraint that the slope of the IMF at $m >= 8$
$M_\odot$ must be consistent with a Kroupa-like IMF. We construct an IMF model
that is a linear combination of a Milky Way-like IMF and a broken power-law
IMF, with a steep slope ($\alpha_1=$ $3.84$) for stars < 0.5 $M_\odot$ (as
suggested by near-IR indices), and that flattens out ($\alpha_2=$ $2.14$) for
stars > 0.5 $M_\odot$, and discuss its wider ramifications and limitations.
