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.
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