  As the pion mass approaches a critical value $m_\pi^\star$ from below, an
$S$-wave resonance crosses pion-baryon threshold and becomes a bound state with
arbitrarily small binding energy, thus driving the scattering length to
diverge. I explore the consequences of chiral symmetry for the values of
$m_\pi$ close to $m_\pi^\star$. It turns out that chiral symmetry is crucial
for an $S$-wave resonance to be able to stand very near threshold and in the
meantime to remain narrow, provided that the mass splitting is reasonably
small. The effective range of pion-baryon scattering is unexpectedly large,
proportional to $ 4\pi f_\pi^2/m_\pi^3$ when $m_\pi$ is around $m_\pi^\star$.
As a result, this unexpected large length scale causes universality relations
to break down much sooner than naively expected.
