We study the asymptotics of the ruin probability in the Cram\'er-Lundberg
model with a modified notion of ruin. The modification is as follows. If the
portfolio becomes negative, the asset is not immediately declared ruined but
may survive due to certain mechanisms. Under a rather general assumption on the
mechanism - satisfied by most such modified models from the literature - we
study the relation of the asymptotics of the modified ruin probability to the
classical ruin probability. This is done under the Cram\'er condition as well
as for subexponential integrated claim sizes.Comment: 9 page
