  For neutrons bound inside nuclei, baryon instability can manifest itself as a
decay into undetectable particles (e.g., $\it n \to \nu \nu \bar{\nu} $), i.e.,
as a disappearance of a neutron from its nuclear state. If electric charge is
conserved, a similar disappearance is impossible for a proton. The existing
experimental lifetime limit for neutron disappearance is 4-7 orders of
magnitude lower than the lifetime limits with detectable nucleon decay products
in the final state [PDG2000]. In this paper we calculated the spectrum of
nuclear de-excitations that would result from the disappearance of a neutron or
two neutrons from $^{12}$C. We found that some de-excitation modes have
signatures that are advantageous for detection in the modern high-mass,
low-background, and low-threshold underground detectors, where neutron
disappearance would result in a characteristic sequence of time- and
space-correlated events. Thus, in the KamLAND detector [Kamland], a
time-correlated triple coincidence of a prompt signal, a captured neutron, and
a $\beta^{+}$ decay of the residual nucleus, all originating from the same
point in the detector, will be a unique signal of neutron disappearance
allowing searches for baryon instability with sensitivity 3-4 orders of
magnitude beyond the present experimental limits.
