  We study the late time behavior of the boundary state representing the
rolling tachyon constructed by Sen. It is found that the coupling of the
rolling tachyon to massive modes of the closed string grows exponentially as
the system evolves. We argue that the description of rolling tachyon by a
boundary state is valid during the finite time determined by string coupling,
and that energy could be dissipated to the bulk beyond this time. We also
comment on the relation between the rolling tachyon boundary state and the
spacelike D-brane boundary state.
