  A recent construction of Hacking relates the classification of stable vector
bundles on a surface of general type with $p_g = 0$ and the boundary of the
moduli space of deformations of the surface. In the present paper we analyze
this relation for Godeaux surfaces. We provide a description of certain
boundary components of the moduli space of Godeaux surfaces. Also we explicitly
construct certain exceptional vector bundles of rank 2 on Godeaux surfaces,
stable with respect to the canonical class, and examine the correspondence
between the boundary components and such exceptional vector bundles.
