  Extensive dynamical $N/D$ calculations are made in the study of $S_{11}$
channel low energy $\pi$N scatterings, based on various phenomenological model
inputs of left cuts at tree level. The subtleties of the singular behavior of
the partial wave amplitude at the origin of the complex $s$ plane are carefully
analysed. Furthermore, { it is found that the dispersion representation for the
phase shift, $\delta$, has to be modified in the case of $\pi $N scatterings.
An additional contribution from the dispersion integral exists, which is,
however, almost exactly cancelled the contribution from two virtual poles
located near the end points of the segment cut induced by $u$ channel nucleon
exchanges.} Relying very little on the details of the dynamical inputs, the
subthreshold resonance $N^*(890)$ survives.
