We investigate, in deep inelastic scattering (DIS) by charged leptons, the numerical importance of semi-inclusive kaon production due to the generalized Sullivan process, in which the virtual photon may strike and smash the recoiling baryon upon meson emission of the target proton, as compared to the standard mechanism in the fragmentation picture of Field and Feynman. Our numerical results indicate that the standard fragmentation picture is modified only in a very limited kinematic region (characterized by very small x, very small y, and z close to unity, with x the Bjorken scaling variable, y the fraction of the energy transfer, and z the momentum fraction carried away by the kaon).