  We show how open strings cease to propagate when unstable D-branes decay. The
information on the propagation is encoded in BSFT two-point functions for
arbitrary profiles of open string excitations. We evaluate them in tachyon
condensation backgrounds corresponding to (i) static spatial tachyon kink (=
lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i)
the propagation is restricted to the directions along the tachyon kink, while
for (ii) all the open string excitations cease to propagate at late time and
are subject to a collapsed light cone characterized by Carrollian contraction
of Lorentz group.
