  Recently, numerical calculations of the magnetic field evolution in neutron
stars demonstrated the possible existence of a Hall attractor, a stage at which
the evolution of the field driven by the Hall cascade ends. The existence of
such a stage in neutron star magnetic evolution is very important, and can be
potentially probed by observations. Here we discuss three types of objects
which could have reached this stage. First, we briefly describe the evolution
of normal radio pulsars with ages about a few hundred thousand years. Then we
analyse in more detail observations of RX J1856.5-3754, one of the Magnificent
Seven, focusing on the surface temperature distribution and comparing model
predictions with the temperature map inferred from X-ray observations. Finally,
we discuss the necessity of the Hall attractor stage to explain the
hypothetical existence of accreting magnetars. We conclude that at the moment
there is no direct confirmation of the Hall attractor stage in known sources.
However, more detailed observations in the near future can demonstrate
existence (or absence) of this stage of the crustal magnetic field evolution.
