  The matrix model formulation of two dimensional string theory has been shown
to admit time dependent classical solutions whose closed string duals are
geodesically incomplete space-times with space-like boundaries. We investigate
some aspects of the dynamics of fermions in one such background. We show that
even though the background solution appears pathological, the time evolution of
the system is smooth in terms of open string degrees of freedom, viz. the
fermions. In particular, an initial state of fermions evolves smoothly into a
well defined final state over an infinite open string time interval, while the
time perceived by closed strings appears to end abruptly. We outline a method
of calculating fermion correlators exactly using symmetry properties. The
result for the two point function is consistent with the semiclassical picture.
