We study the dynamics and observational signatures of a neutron star being consumed by a much less massive black hole residing inside the star. This phenomenon could arise in a variety of scenarios, including after the capture of a primordial black hole, or in some models of asymmetric dark matter where the dark matter particles collect at the center of a neutron star and eventually collapse to form a black hole. However, the details of how the neutron star implodes are not well known, which is crucial to determining the observational implications of such events. We utilize fully general relativistic simulations to follow the evolution of such a black hole as it grows by several orders of magnitude, and ultimately consumes the neutron star. We consider a range of spin values for the neutron star, from non-rotating stars, to those with millisecond periods, as well as different equations of state. We find that as the black hole grows, it obtains a non-negligible spin and induces differential rotation in the core of the neutron star. In contrast to previous studies, we find that the amount of dynamical ejecta is very small, even for rapidly rotating stars, dampening the prospects for producing a kilonova-type electromagnetic signal from such events. We comment on other possible electromagnetic and gravitational signals.arXiv:1909.07968v1 [gr-qc]