  Vector bundles in positive characteristics have a tendency to be destabilized
after pulling back by the Frobenius morphism. In this paper, we closely examine
vector bundles over curves that are, in an appropriate sense, maximally
destabilized by the Frobenius morphism. Then we prove that such bundles of rank
2 exist over any curve in characteristic 3, and are unique up to twisting by a
line bundle. We also give an application of such bundles to the study of ample
vector bundles, which is valid in all characteristics.
