  We investigate convergence of point processes associated with critical faces
for a \v{C}ech filtration built over a homogeneous Poisson point process in the
$d$-dimensional flat torus. The convergence of our point process is established
in terms of the $\mathcal M_0$-topology, when the connecting radius of a
\v{C}ech complex decays to $0$, so slowly that critical faces are even less
likely to occur than those in the regime of threshold for homological
connectivity. We also obtain a series of limit theorems for positive and
negative critical faces, all of which are considerably analogous to those for
critical faces.
