  The observational manifestation of a neutron star is strongly connected with
the properties of its magnetic field. During the star's lifetime, the field
strength and its changes dominate the thermo-rotational evolution and the
source phenomenology across the electromagnetic spectrum. Signatures of
magnetic field evolution are best traced among elusive groups of X-ray emitting
isolated neutron stars (INSs), which are mostly quiet in the radio and
$\gamma$-ray wavelengths. It is thus important to investigate and survey INSs
in X-rays in the hope of discovering peculiar sources and the long-sought
missing links that will help us to advance our understanding of neutron star
evolution. The Extended R\"ontgen Survey with an Imaging Telescope Array
(\eROS), the primary instrument on the forthcoming Spectrum-RG mission, will
scan the X-ray sky with unprecedented sensitivity and resolution. The survey
has thus the unique potential to unveil the X-ray faint end of the neutron star
population and probe sources that cannot be assessed by standard pulsar
surveys.
