  We develop a general approach for studying the cumulative probability
distribution function of localized objects (particles) whose dynamics is
governed by the first-order Langevin equation driven by superheavy-tailed
noise. Solving the corresponding Fokker-Planck equation, we show that due to
this noise the distribution function can be divided into two different parts
describing the surviving and absorbing states of particles. These states and
the role of superheavy-tailed noise are studied in detail using the theory of
slowly varying functions.
