  We study how light scalar fields can change the stellar landscape by
triggering a new phase of nuclear matter. Scalars coupled to nucleons can
develop a non-trivial expectation value at finite baryon density. This sourcing
of a scalar reduces the nucleon mass and provides an additional energy density
and pressure source. Under generic conditions, a new ground state of nuclear
matter emerges, with striking implications for the configuration of stellar
remnants. Notably, neutron stars in the new ground state can be significantly
heavier than QCD equations of state currently predict. We also find hybrid
stellar compositions and stable self-bound objects with sizes as small as the
Compton wavelength of the scalar. We discuss several specific realizations of
this scenario: the QCD axion and lighter generalizations thereof and linearly
or quadratically coupled scalar fields effectively equivalent to a class of
scalar-tensor modification of gravity. Lastly, we explore phenomenological
signatures relevant to electromagnetic and gravitational wave observations of
neutron stars, such as atypical compactness and instability gaps in radii.
