  Starting from the amplitude with an arbitrary number of massless closed
states of the bosonic string, we compute the soft limit when one of the states
becomes soft to subsubleading order in the soft momentum expansion, and we show
that when the soft state is a graviton or a dilaton, the full string amplitude
can be expressed as a soft theorem through subsubleading order. It turns out
that there are string corrections to the field theoretical limit in the case of
a soft graviton, while for a soft dilaton the string corrections vanish. We
then show that the new soft theorems, including the string corrections, can be
simply obtained from the exchange diagrams where the soft state is attached to
the other external states through the three-point string vertex of three
massless states. In the soft-limit, the propagator of the exchanged state is
divergent, and at tree-level these are the only divergent contributions to the
full amplitude. However, they do not form a gauge invariant subset and must be
supplemented with extra non-singular terms. The requirement of gauge invariance
then fixes the complete amplitude through subsubleading order in the soft
expansion, reproducing exactly what one gets from the explicit calculation in
string theory. From this it is seen that the string corrections at
subsubleading order arise as a consequence of the three-point amplitude having
string corrections in the bosonic string. When specialized to a soft dilaton,
it remarkably turns out that the string corrections vanish and that the
non-singular piece of the subsubleading term of the dilaton soft theorem is the
generator of space-time special conformal transformation.
