  We report a $^{63}$Cu NMR investigation in detwinned YBa$_2$Cu$_3$O$_y$
single crystals, focusing on the highly underdoped regime (y=6.35-6.6).
Measurements of both the spectra and the spin-lattice relaxation rates of
$^{63}$Cu uncover the emergence of static order at a well-defined onset
temperature $T_0$ without a known order parameter as yet. While $T_0$ is
rapidly suppressed with increasing hole doping concentration $p$, the spin
pseudogap was identified only near and above the doping content at which
$T_0\rightarrow 0$. Our data indicate the presence of a critical hole doping
$p_c\sim 0.1$, which may control both the static order at $p<p_c$ and the spin
pseudogap at $p>p_c$.
