The off-shell behaviors of bound nucleons in deep inelastic lepton nucleus scattering are discussed in two scenarios with the basic constituents chosen to be baryon-mesons and quark-gluons respectively in light-cone formalism. It is found that when taking into account the effect due to internal quark structure of nucleons, the derived scaling variable for bound nucleons and the calculated nuclear structure functions are different from those in considering the baryon-mesons as the effective elementary constituents. This implies that the pure baryon-meson descriptions of nuclei give the inaccurate off-shell behavior of the bound nucleon structure function, thereby the quark-gluons seem to be the most appropriate degrees of freedom for nuclear descriptions.