  The results of background measurements with the second version of the
BOREXINO Counting Test Facility (CTF-II), installed in the Gran Sasso
Underground Laboratory, were used to obtain limits on the instability of
nucleons, bounded in nuclei, for decays into invisible channels ($inv$):
disappearance, decays to neutrinos, etc. The approach consisted of a search for
decays of unstable nuclides resulting from $N$ and $NN$ decays of parents
$^{12}$C, $^{13}$C and $^{16}$O nuclei in the liquid scintillator and the water
shield of the CTF. Due to the extremely low background and the large mass (4.2
ton) of the CTF detector, the most stringent (or competitive) up-to-date
experimental bounds have been established: $\tau(n \to inv) > 1.8 \cdot
10^{25}$ y, $\tau(p \to inv) > 1.1 \cdot 10^{26}$ y, $\tau(nn \to inv) > 4.9
\cdot 10^{25}$ y and $\tau(pp \to inv) > 5.0 \cdot 10^{25}$ y, all at 90% C.L.
