We study a new mode of the neutrinoless and two-neutrino double-beta decays in which a single electron is emitted from the atom. The other electron is assumed to occupy one of the vacant s1/2 or p1/2 subshells of the daughter ion. Such process could manifest itself through an additional background signal in the single-electron spectra, which will be accessible in the next-generation experiment SuperNEMO. We calculate the phase-space factors in terms of relativistic electron wave functions obtained as the solutions to the Dirac equation and evaluated at the nuclear radius, while taking into account the shielding effect of nuclear charge via the multiconfiguration Dirac–Hartree–Fock package Grasp2K. Half-lives are estimated for the most relevant double-beta-decay isotopes and experimental significance is discussed.