  In this paper, we study the gravitational collapse of null dust in the
cylindrically symmetric spacetime. The naked singularity necessarily forms at
the symmetry axis. We consider the situation in which null dust is emitted
again from the naked singularity formed by the collapsed null dust and
investigate the back-reaction by this emission for the naked singularity. We
show a very peculiar but physically important case in which the same amount of
null dust as that of the collapsed one is emitted from the naked singularity as
soon as the ingoing null dust hits the symmetry axis and forms the naked
singularity. In this case, although this naked singularity satisfies the strong
curvature condition by Kr\'{o}lak (limiting focusing condition), geodesics
which hit the singularity can be extended uniquely across the singularity.
Therefore we may say that the collapsing null dust passes through the
singularity formed by itself and then leaves for infinity. Finally the
singularity completely disappears and the flat spacetime remains.
