We investigate Λ production in semi-inclusive deep-inelastic scattering using a polarized lepton beam and find that the spin transfer is significantly suppressed by target fragmentation. As further demonstrated by a model estimation, experimental data can be well described once the target fragmentation is taken into account, which alleviates the tension with calculations solely based on current fragmentation. Our findings suggest that, at the energies of existing fixed-target experiments, the separation of current and target fragmentation regions is not distinct. Spin transfer as well as other spin effects offers a sensitive probe into the origin of the produced hadron.