Coexistence of metallicity and ferroelectricity has been a curiosity without a practical application, both because free-electron screening due to metallicity prevents the polarization from being switched by an electric field, diminishing the value of ferroelectricity, and because metallicity is usually achieved by doping, which leads to disorder and is often detrimental to other electronic properties. Here, we predict via first-principles calculation a switchable metallic ferroelectric barrier in ${({\mathrm{Co}}_{2})}_{9}\text{\ensuremath{-}}{\mathrm{TiO}}_{2}\text{\ensuremath{-}}{(\mathrm{BaO}\text{\ensuremath{-}}{\mathrm{TiO}}_{2})}_{m}\text{\ensuremath{-}}\mathrm{CoO}\text{\ensuremath{-}}\mathrm{Co}\phantom{\rule{4pt}{0ex}}(m=4,5,6,7,8,9)$ multiferroic tunnel junction without doping. The metallic ferroelectricity is caused by an electrode proximity effect that is common to ionic ferroelectric materials and shifts the Fermi energy as a function of the termination layer at the interfaces. This effect is accentuated by the large polarization of the CoO layer relatively to that of ${\mathrm{BaTiO}}_{3}$ (BTO), leading to a larger electrostatic potential drop on the interface containing CoO, thus further pulling the conduction band bottom of the entire BTO region below the Fermi energy. Increasing the polarization of BTO relative to that of CoO, e.g., by applying strain, can remove the metallicity, allowing the polarization to be switched electrically. Switching between metallic and insulating states by controlling ferroelectric polarization leads to a large tunneling electroresistance.