There is a subtle distinction between confinement and a bosonic bound state with a mass gap.

Take for example BCS theory of superconductivity. The cooper pair is a bosonic bound state consists of spin up and spin down electrons. Does it imply all electrons are confined in cooper pairs? Not necessarily so. After Bogoliubov transformation, you can arrive at a well-defined single fermion propagator, which indicates that electrons are not totally confined.

And for that matter, practically all models of effective four-fermion interactions exhibit this sort of dynamical chiral symmetry breaking behavior devoid of confinement. These includes NJL model and the 2D Gross-Neveu model you mentioned.

There is a subtle distinction between confinement and a bosonic bound state with a mass gap.

Take for example BCS theory of superconductivity. The cooper pair is a bosonic bound state consists of spin up and spin down electrons. Does it imply all electrons are confined in cooper pairs? Not necessarily so. After Bogoliubov transformation, you can arrive at a well-defined single fermion propagator, which indicates that electrons are not totally confined.

And for that matter, practically all models of effective four-fermion interactions exhibit this sort of dynamical symmetry breaking behavior devoid of confinement. These includes NJL model and the 2D Gross-Neveu model (involving chiral symmetry breaking condensation of left- and right-handed fermion pairs) you mentioned.

A home work question: The hydrogen atom is a bosonic bound state of a proton and a electron. Does it indicate confinement of protons and electrons?