  We study pairs of planar D-branes intersecting on null hypersurfaces, and
other related configurations. These are supersymmetric and have finite energy
density. They provide open-string analogues of the parabolic orbifold and
null-fluxbrane backgrounds for closed superstrings. We derive the spectrum of
open strings, showing in particular that if the D-branes are shifted in a
spectator dimension so that they do not intersect, the open strings joining
them have no asymptotic states. As a result, a single non-BPS excitation can in
this case catalyze a condensation of massless modes, changing significantly the
underlying supersymmetric vacuum state. We argue that a similar phenomenon can
modify the null cosmological singularity of the time-dependent orbifolds. This
is a stringy mechanism, distinct from black-hole formation and other strong
gravitational instabilities, and one that should dominate at weak string
coupling. A by-product of our analysis is a new understanding of the appearance
of 1/4 BPS threshold bound states, at special points in the moduli space of
toroidally-compactified type-II string theory.
