  Bound-systems of $\Xi^-$--$^{14}_{}{\rm N}$ are studied via $\Xi^-$ capture
at rest followed by emission of a twin single-$\Lambda$ hypernucleus in the
emulsion detectors. Two events forming extremely deep $\Xi^-$ bound states were
obtained by analysis of a hybrid method in the E07 experiment at J-PARC and
reanalysis of the E373 experiment at KEK-PS. The decay mode of one event was
assigned as $\Xi^-+^{14}_{}{\rm N}\to^{5}_{\Lambda}{\rm
He}$+$^{5}_{\Lambda}{\rm He}$+$^{4}_{}{\rm He}$+n. Since there are no excited
states for daughter particles, the binding energy of the $\Xi^-$ hyperon,
$B_{\Xi^-}$, in $^{14}_{}{\rm N}$ nucleus was uniquely determined to be 6.27
$\pm$ 0.27 MeV. Another $\Xi^-$--$^{14}_{}{\rm N}$ system via the decay
$^{9}_{\Lambda}{\rm Be}$ + $^{5}_{\Lambda}{\rm He}$ + n brings a $B_{\Xi^-}$
value, 8.00 $\pm$ 0.77 MeV or 4.96 $\pm$ 0.77 MeV, where the two possible
values of $B_{\Xi^-}$ correspond to the ground and the excited states of the
daughter $^{9}_{\Lambda}{\rm Be}$ nucleus, respectively. Because the
$B_{\Xi^-}$ values are larger than those of the previously reported events
(KISO and IBUKI), which are both interpreted as the nuclear $1p$ state of the
$\Xi^-$--$^{14}_{}{\rm N}$ system, these new events give the first indication
of the nuclear $1s$ state of the $\Xi$ hypernucleus, $^{15}_{\Xi}{\rm C}$.
