  Near-solar mass black holes (BHs) could have been involved in the two recent
gravitational wave events, GW190425 and GW190814. Since such a low mass BH
cannot be formed via stellar evolution, a model has been proposed based on the
core collapse of a neutron star initiated by a certain number of dark matter
(DM) particles. In this process, the accumulated DM particles collapse to form
a tiny BH inside the neutron star, and the entire neutron star is transmuted
into a BH after a certain time due to the accretion of matter by the
endoparasitic BH from its host. Here, we argue that, depending on the initial
conditions, a dark core collapse could give rise to either a BH or a naked
singularity. For example, if the accumulated cloud of DM particles in the core
of a neutron star can be modeled as an anisotropic fluid and it fulfils the
criterion for collapse, an endoparasitic naked singularity could form instead
of an endoparasitic BH. Immediately after its formation, the naked singularity
should begin accreting matter from the host neutron star, thus eventually
transmuting the entire host into a near-solar mass, relatively slowly-spinning
naked singularity. We also propose a general technique to constrain the DM
particle--neutron scattering cross section using the lack of pulsars near the
Galactic centre and assuming that these missing pulsars have already been
transmuted into BHs and/or naked singularities. Thus, the missing pulsars also
indicate the existence of many such singularities near the Galactic center.
