  As proposed recently by Fornal and Grinstein, neutrons can undergo a dark
matter decay mode which was not observed before. Such a decay could explain the
existing discrepancy between two different methods of neutron lifetime
measurements. If such neutron decay is possible, then it should occur also is
nuclei with sufficiently low neutron binding energy. We examine a few nuclear
candidates for the dark neutron decay and we consider possibilities of their
experimental identification. In more detail we discuss the case of $^{11}$Be
which appears as the most promising nucleus for the observation of the neutron
dark decay.
