  An ultraviolet cutoff dependent on the chemical potential as proposed by
Casalbuoni {\it et al} is used in the su(3) Nambu-Jona-Lasinio model. The model
is applied to the description of stellar quark matter and compact stars. It is
shown that with a new cutoff parametrization it is possible to obtain stable
hybrid stars with a quark core. A larger cutoff at finite densities leads to a
partial chiral symmetry restoration of quark $s$ at lower densities. A direct
consequence is the onset of the $s$ quark in stellar matter at lower densities
and a softening of the equation of state.
