We conducted measurements of $K^- + {^3{\rm He}} \to \pi \!Y \!N + N'$ reactions using $1~{\rm GeV}/c$ $K^-$-beam, aiming to understand the broad decay width of $\bar{K} \!N \!N$ ($\approx$ twice as broad as that of $\Lambda(1405)$ considered to be the $\bar{K} \!N$ quasi-bound state). We successfully reproduced distributions of the $\pi \! Y \! N$ invariant mass and momentum transfer of $\pi \! Y \! N$ by employing model fitting functions for $\bar{K} \! N \! N$ formation and quasi-free $\bar{K}$ absorption (${\rm QF}_{\bar{K}-{\rm abs}}$) processes. The model can describe the experimental data quite well, and four $\bar{K} \! N \! N \to \pi \! Y \! N $ cross-sections were obtained. The result suggests that the mesonic decay is the dominant decay branch of $\bar{K} \! N \! N$. It was also suggested that $\Gamma_{\pi \Lambda N} \sim \Gamma_{\pi \Sigma N}$, which indicates a significant contribution of the $I_{\bar{K} \! N}=1$ absorption channel to the $\bar{K} \! N \! N$ decay as well as the $I_{\bar{K} \! N}=0$ makes the $\bar{K} \! N \! N$ state $\approx$ twice as unstable as $\Lambda$(1405).