  In this note we reexamine the possibility of constructing stable
non-supersymmetric theories that exhibit an exponential density of states. For
weakly coupled closed strings there is a general theorem, according to which
stable theories with an exponential density of states must exhibit an almost
exact cancellation of spacetime bosons and fermions (not necessarily level by
level). We extend this result to open strings by showing that if the above
cancellation between bosons and fermions does not occur, the open strings do
not decouple from a closed string tachyon even in the NCOS scaling limit. We
conclude with a brief comment on the proposed generalization of the AdS/CFT
correspondence to non-supersymmetric theories.
