  The Standard Model of Particle Physics predicts the double-$\beta$ decay of
certain nuclei with the emission of two active neutrinos. In this letter, we
argue that double-$\beta$ decay experiments could be used to probe models with
light exotic fermions through the search for spectral distortions in the
electron spectrum with respect to the Standard Model expectations. We consider
two concrete examples: models with light sterile neutrinos, singly produced in
the double-$\beta$ decay, and models with a light $Z_2$-odd fermion, pair
produced due to a $Z_2$ symmetry. We estimate the discovery potential of a
selection of double-$\beta$ decay experiments and find that future searches
will test for the first time a new part of the parameter space of interest at
the MeV-mass scale.
