Whether or not such a collapsing object forms a black hole depends on the specific properties of the object. In some cases, an object may be very close to the threshold, having a hard time deciding whether or not to form a black hole.
Talk about tottering on the very edge of the infinite abyss itself!
I wonder what would happen if you zoom in on the math of that moment when the object finally commits, on the very boundary between relativity and particle physics, at the Planck scales they might be able to steal a glimpse or two of gravity handshaking the quantum world.
EDIT: ...or splintering into an infinity of pieces, again.