  The aim of this paper is to investigate the transition of a strongly
magnetized neutron star into the accretion regime with very low accretion rate.
For this purpose we monitored the Be-transient X-ray pulsar GRO J1008-57
throughout a full orbital cycle. The current observational campaign was
performed with the Swift/XRT telescope in the soft X-ray band (0.5-10 keV)
between two subsequent Type I outbursts in January and September 2016. The
expected transition to the propeller regime was not observed. However, the
transitions between different regimes of accretion were detected. In
particular, after an outburst the source entered a stable accretion state
characterised by the accretion rate of ~10^14-10^15 g/s. We associate this
state with accretion from a cold (low-ionised) disc of temperature below ~6500
K. We argue that a transition to such accretion regime should be observed in
all X-ray pulsars with certain combination of the rotation frequency and
magnetic field strength. The proposed model of accretion from a cold disc is
able to explain several puzzling observational properties of X-ray pulsars.
