  For a Landau-Zener transition in a two-level system, the probability for a
particle, initially in the first level, {\em i}, to survive the transition and
to remain in the first level, depends exponentially on the square of the tunnel
matrix element between the two levels. This result remains valid when the
second level, {\em f}, is broadened due to e.g. coupling to continuum [V. M.
Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. If the level,
{\em i}, is also coupled to continuum, albeit much weaker than the level {\em
f}, a particle, upon surviving the transition, will eventually escape. However,
for shorter times, the probability to find the particle in the level {\em i}
after crossing {\em f} is {\em enhanced} due to the coupling to continuum.
This, as shown in the present paper, is the result of a second-order process,
which is an {\em additional coupling between the levels}. The underlying
mechanism of this additional coupling is virtual tunneling from {\em i} into
continuum followed by tunneling back into {\em f}.
