Supernova happens when neutron star is created. Neutrons prevent further collapse. Size about that of a large city. Highest mass core shrinks to a point. On the way to total collapse it may momentarily create a neutron star and the resulting supernova rebound explosion.
Gravity finally wins.
Nothing holds it up. Space so warped around the object that it effectively leaves our space. Details about the remnants are given in the Stellar Remnants section below. Elements heavier than Iron are made in supernova explosion. Lowest mass stars can only synthesize Helium.