© 2018 American Physical Society. Ferroelectric materials are characterized by a spontaneous polar distortion. The behavior of such distortion in the presence of free charge is the key to the physics of metallized ferroelectrics in particular, and of structurally polar metals more generally. Using first-principles simulations, here we show that a polar distortion resists metallization and the attendant suppression of long-range dipolar interactions in the vast majority of a sample of 11 representative ferroelectrics. We identify a meta-screening effect, occurring in the doped compounds as a consequence of the charge rearrangements associated to electrostatic screening, as the main factor determining the survival of a noncentrosymmetric phase. Our findings advance greatly our understanding of the essentials of structurally polar metals, and offer guidelines on the behavior of ferroelectrics upon field-effect charge injection or proximity to conductive device elements.