  In perturbative string theory, one is generally interested in asymptotic
observables, such as the S-matrix in flat spacetime, and boundary correlation
functions in anti-de Sitter spacetime. However, there are backgrounds in which
such observables do not exist. We study examples of such backgrounds in 1+1
dimensional string theory. In these examples, the Liouville wall accelerates
and can become spacelike in the past and/or future. When that happens, the
corresponding null infinity, at which the standard scattering states are
defined, is shielded by the Liouville wall. We compute scattering and particle
production amplitudes in these backgrounds in the region in parameter space
where the wall remains timelike, and discuss the continuation of this picture
to the spacelike regime. We also discuss the physics from the point of view of
the dynamics of free fermions in backgrounds with a time-dependent Fermi
surface.
