We present the expected X-ray polarization signal resulting from distant reprocessing material around black holes. Using a central isotropic power-law emission at the center of the simulated model, we add distant equatorial and axially symmetric media that are covering the central accreting sources. We include partial ionization and partial transparency effects, and the impact of various polarization and steepness of the primary radiation spectrum. The results are obtained with the Monte Carlo code STOKES that considers both line and continuum processes and computes the effects of scattering and absorption inside static homogenous wedge-shaped and elliptical toroidal structures, varying in relative size, composition and distance to the source. We provide first order estimates for parsec-scale reprocessing in Compton-thin and Compton-thick active galactic nuclei, as well as winds around accreting stellar-mass compact objects. The resulting polarization can reach tens of % with either parallel or perpendicular orientation with respect to the axis of symmetry, depending on subtle details of the geometry, density and ionization structure. We also show how principal parameters can be constrained from X-ray spectroscopy or polarimetry in other wavelengths to lift the shown degeneracies in the X-ray band. We provide an application example of the broad modelling discussion by revisiting the recent IXPE 2-8 keV X-ray polarimetric observation of the accreting stellar-mass black hole in Cygnus X-3 from the perspective of partial transparency and ionization of the obscuring outflows.