  X-ray observations of active galactic nuclei (AGN) show variability on
timescales ranging from a few hours up to a few days. Some of this variability
may be associated with occultation events by clouds in the broad line region.
In this work, we aim to model the spectral and polarization variability arising
from X-ray obscuration events, serving as probes of the relativistic effects
that dominate the emission from the innermost regions. We show that asymmetries
can be clearly detected in the AGN spectra as the cloud is shading different
parts of the accretion disc. We also show that these effects can be detected in
the temporal evolution of the polarization degree ($P$) and the polarization
position angle ($\Psi$). The variations in $P$ and $\Psi$ are highly dependent
on the inclination of the system, the position of the primary source and its
intrinsic polarization. Considering the disc-corona system only, for an
inclination $\theta = 30^\circ$ (60$^\circ$), $P$ increases up to $\sim 20$%
(30)%, in the 4-8 keV band, when the unpolarized primary source is obscured.
However, after accounting for the contribution of parsec-scale material
scattering the light in our line of sight (narrow-line region and molecular
torus), the variability is smoothed out and the polarization degree can be
reduced down to $\sim 1$% (2%). Our results suggest that the study of eclipses
in AGN with the next generation of X-ray spectral and polarimetric missions
could provide unique information on the physics and structure of the innermost
regions as well as of the parsec-scale material.
