  We show that the mass-radius $(M-R)$ relation corresponding to the stiffest
equation of state (EOS) does not provide the necessary and sufficient condition
of dynamical stability for the equilibrium configurations, since such
configurations can not satisfy the `compatibility criterion'. In this
connection, we construct sequences composed of core-envelope models such that,
like the stiffest EOS, each member of these sequences satisfy the extreme case
of causality condition, $v = c = 1$, at the centre. We, thereafter, show that
the $M-R$ relation corresponding to the said core-envelope model sequences can
provide the necessary and sufficient condition of dynamical stability only when
the `compatibility criterion' for these sequences is `appropriately' satisfied.
However, the fulfillment of `compatibility criterion' can remain satisfied even
when the $M-R$ relation does not provide the necessary and sufficient condition
of dynamical stability for the equilibrium configurations.
  In continuation to the results of previous study, these results explicitly
show that the `compatibility criterion' {\em independently} provides, in
general, the {\em necessary} and {\em sufficient} condition of hydrostatic
equilibrium for any regular sequence. Beside its fundamental feature, this
study can also explain simultaneously, both (the higher as well as lower)
values of the glitch healing parameter observed for the Crab and the Vela-like
pulsars respectively, on the basis of starquake model of glitch generation.
