It has been known for decades that a ferromagnetic sample can depolarize a transmitted neutron beam. This effect was used and developed into the neutron-depolarization technique to investigate the magnetic structure of ferromagnetic materials. Since the polarization evolves continuously as the neutrons move through the sample, the initial spin states on scattering will be different at different depths within the sample. This leads to a contamination of the measured spin-dependent neutron-scattering intensities by the other spin-dependent cross sections. The effect has rarely been considered in polarized neutron-scattering experiments even though it has a crucial impact on the observable signal. A model is proposed to describe the depolarization of a neutron beam traversing a ferromagnetic sample, provide the procedure for data correction and give guidelines to choose the optimum sample thickness. It is experimentally verified for a small-angle neutron-scattering geometry with samples of the nanocristalline soft-magnet Vitroperm (Fe₇₃Si₁₆B₇Nb₃Cu₁). The model is general enough to be adapted to other types of neutron-diffraction experiments and sample geometries.