A general formulation is developed to demonstrate that atomic autoionizing (AI) resonances are broadened and shifted significantly due to plasma effects across bound-free continua. The theoretical and computational method presented accounts for broadening mechanisms: electron collisional, ion microfields (Stark), thermal Doppler, core excitations, and free-free transitions. Extrinsic plasma broadening redistributes and shifts AI resonance strengths while broadly preserving naturally intrinsic asymmetries of resonance profiles. Integrated oscillator strengths are conserved as resonance structures dissolve into continua with increasing electron density. As exemplar, the plasma attenuation of photoionization cross sections computed using the R-matrix method is studied in neon-like Fe XVII in a critical range N e = 10 21−24 cc along isotherms T = 1 − 2 × 10 6 K, and its impact on Rosseland Mean opacities. The energy-temperature-density dependent cross sections would elicit and introduce physical features in resonant processes in photoionization, (e + ion) excitation and recombination. The method should be generally applicable to atomic species in high-energy-density (HED) sources such as fusion plasmas and stellar interiors.Whereas the main broadening mechanisms in AI broadening are physically similar to line broadening, their theoretical and computational treatment is quite different. Superimposed on intrinsic AI broadening in atomic cross sections the extent of resonances owing to extrinsic plasma effects renders much of the line broadening theory inapplicable, particularly for multi-electron systems. The unbroadened AI resonances themselves vary by orders of magnitude in width, shapes and heights, and incorporate two types: large features due to photoexcitation-of-core (PEC) below thresholds corresponding to dipole core transitions [10], and infinite Rydberg series of resonances converging on to each excited core level of the (e + ion) system. The generally employed Voigt line profiles obtained by convolution of a Lorentzian function for radiative and collisional broadening, and a Gaussian function for Doppler or thermal broadening, are found to be practically inapplicable for AI broadening. Numerically, the Voigt kernel is ill-conditioned since the collisional-to-Doppler width ratio Γ c /Γ d varies over a far wider range for resonances than lines and therefore unconstrained a priori [11,12].