The solitonic sector of the Nambu-Jona-Lasinio model with baryon numbe
r one is solved in the presence of an external medium. The calculation
s fully include the polarization of both the Dirac sea and the medium
as well as the Pauli-blocking effect. We found that with an increasing
density the medium destabilizes the soliton. At finite medium density
the soliton mass gets reduced whereas the mean-square baryon radius s
hows an increase - a swelling of the soliton. At some critical density
of about two times nuclear matter density there is no localized solut
ion - the soliton disappears.