  It is uncertain whether or not low-mass Population III stars ever existed.
While limits on the number density of Population III stars with $M_{\ast}
\approx 0.8~M_{\odot}$ have been derived using Sloan Digital Sky Survey (SDSS)
data, little is known about the occurrence of Population III stars at lower
masses. In the absence of reliable parallaxes, the spectra of metal-poor main
sequence (MPMS) stars with $M_{\ast} \lesssim 0.8~M_{\odot}$ can easily be
confused with cool white dwarfs. To resolve this ambiguity, we present a
classifier that differentiates between MPMS stars and white dwarfs based on
photometry and/or spectroscopy without the use of parallax information. We
build and train our classifier using state-of-the-art theoretical spectra and
evaluate it on existing SDSS-based classifications for objects with reliable
Gaia DR2 parallaxes. We then apply our classifier to a large catalog of objects
with SDSS photometry and spectroscopy to search for MPMS candidates. We
discover several previously unknown candidate extremely metal-poor (EMP) stars
and recover numerous confirmed EMP stars already in the literature. We conclude
that archival SDSS spectroscopy has already been exhaustively searched for EMP
stars. We predict that the lowest-mass primordial-composition stars will have
redder optical-to-infrared colors than cool white dwarfs at constant effective
temperature due to surface gravity-dependent collision-induced absorption from
molecular hydrogen. We suggest that the application of our classifier to data
produced by next-generation spectroscopic surveys will set stronger constraints
on the number density of low-mass Population III stars in the Milky Way.
