Traditionally, the formation of off-stoichiometric compounds is believed to be the growth effect rather than the intrinsic tendency of the system. However, here, using the example of La3Te4, we demonstrate that in n-type gapped metals having a large internal gap between principal band edges and the Fermi level inside of the principal conduction band, Fermi-level instability can develop, resulting in a decrease in the formation energy for acceptor defects. Specifically, La vacancies in La3Te4 form spontaneously to produce the acceptor states and remove a fraction of free carriers from the principal conduction band via electron-hole recombination. Such a unique self-doping mechanism allows stabilization of a range of off-stoichiometric La3-xTe4 compounds, which have different electronic properties. Moreover, we thus show how controlling synthesis conditions can be used as a knob to reach the target functionality, including the controllable metal-to-insulator transition.