A black hole doesn't necessarily need to form from a star; theoretically, it could form from any extremely dense object. In fact, many astronomers differentiate certain black holes, like supermassive ones, from stellar ones (ones that form from stars).
However, could the same apply for neutron stars? Neutron stars only form because of the intense gravity during a star's collapse: electron capture is forced to happen, and the majority of the star becomes neutrons. Could this potentially happen to non-stellar objects, if the gravity forces electron capture?
If so, why don't we see as many of these "neutron objects" as we do non-stellar black holes?