  A subcritical branching process in random environment (BPRE) is considered
whose associated random walk does not satisfy the Cramer condition. The
asymptotics for the survival probability of the process is investigated, and a
Yaglom type conditional limit theorem is proved for the number of particles up
to moment $n$ given survival to this moment. Contrary to other types of
subcritical BPRE, the limiting distribution is not discrete. We also show that
the process survives for a long time owing to a single big jump of the
associate random walk accompanied by a population explosion at the beginning of
the process.
