  We calculate the survival probability of a stationary target in one dimension
surrounded by diffusive or subdiffusive traps of time-dependent density. The
survival probability of a target in the presence of traps of constant density
is known to go to zero as a stretched exponential whose specific power is
determined by the exponent that characterizes the motion of the traps. A
density of traps that grows in time always leads to an asymptotically vanishing
survival probability. Trap evanescence leads to a survival probability of the
target that may be go to zero or to a finite value indicating a probability of
eternal survival, depending on the way in which the traps disappear with time.
