As the supergiant star expands, in its ``death throws'', its outer atmosphere
extends far enough away that it literally is pulled away from the star to instead
revolve around the compact object (black hole or neutron star). It takes a while
for the matter to fall all the way into the center, and meanwhile creates a large
extensive disk of material.
How a Supergiant Companion can effect a Neutron Star or Black Hole (compact object):
Most stars are born in binary systems. If a binary pair survives
after the more massive of the two goes Supernova, then we are left with a
compact object (neutron star or black hole) in orbit around a normal star.
Just as we saw Nova and Supernova being created from White Dwarfs in orbit
around Red Giants, Neutron Stars or Black Holes can become detected if they
have a binary companion willing to feed their enourmous gravitational
potential.