  It is commonly believed that black holes are the smallest self-gravitating
objects of the same mass in the Universe. Here, we demonstrate, in a subclass
of higher-order pure gravities known as quasi-topological gravity, that by
modifying general relativity (GR) to reduce the strength of gravity in
strong-field regimes while keeping GR unchanged in weak-field regimes, it is
possible for stars to collapse to radii less than $2M$ while still maintaining
equilibrium between gravity and pressure gradients, leading to
physically-reasonable neutron stars smaller in size than a black hole of the
same mass. We present concrete solutions for such objects and discuss some of
their observational consequences. These objects may furnish new avenues for
understanding the nature of gravity in strong-field regimes and leave imprints
on gravitational wave echoes from compact binary mergers. An observation of
these imprints may constitute evidence for new physics beyond GR when effects
of gravity in strong-field regimes are concerned.
