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.
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