Not even neutron degeneracy can save them. In other words, they fall into themselves. They fall in so much and the gravitational pull is so great, that not even light can escape. Cygnus X-1 located just northeast of Eta Cygni . Another black hole candidate V4641 Sgr is probably one of the closest known at just a mere 1500 light years distant.
Most galaxies have black holes at their centers.