  We investigate the dynamical stability of relativistic, differentially
rotating, quasi-toroidal models of neutron stars through hydrodynamical
simulations in full general relativity. We find that all quasi-toroidal
configurations studied in this work are dynamically unstable against the growth
of non-axisymmetric modes. Both one-arm and bar mode instabilities grow during
their evolution. We find that very high rest mass configurations collapse to
form black holes. Our calculations suggest that configurations whose rest mass
is less than the binary neutron star threshold mass for prompt collapse to
black hole transition dynamically to spheroidal, differentially rotating stars
that are dynamically stable, but secularly unstable. Our study shows that the
existence of extreme quasi-toroidal neutron star equilibrium solutions does not
imply that long-lived binary neutron star merger remnants can be much more
massive than previously found. Finally, we find models that are initially
supra-Kerr ($J/M^2>1$) and undergo catastrophic collapse on a dynamical
timescale, in contrast to what was found in earlier works. However, cosmic
censorship is respected in all of our cases. Our work explicitly demonstrates
that exceeding the Kerr bound in rotating neutron star models does not imply
dynamical stability.
