  We theoretically analyze the $K^{-} {}^{3} \text{He} \to \Lambda p n$
reaction for the $\bar{K} N N$ bound-state search in the J-PARC E15 experiment.
We find that, by detecting a fast and forward neutron in the final state, an
almost on-shell $\bar{K}$ is guaranteed, which is essential to make a bound
state with two nucleons from ${}^{3} \text{He}$. Then, this almost on-shell
$\bar{K}$ can bring a signal of the $\bar{K} N N$ bound state in the $\Lambda
p$ invariant-mass spectrum, although it inevitably brings a kinematic peak
above the $\bar{K} N N$ threshold as well. As a consequence, we predict two
peaks across the $\bar{K} N N$ threshold in the spectrum: the lower peak coming
from the $\bar{K} N N$ bound state, and the higher one originating from the
kinematics.
