For soft solids with their low modulus, small stress already results in large strain, which may cause nonlinearity and yielding. These potentially competing effects were studied on a clay/polybutadiene (clay/sPB) composite, which is a soft physical gel. Structural changes were introduced by oscillatory shear using large amplitude (LAOS). LAOS beyond a critical limit reduced the internal connectivity. This softened the already soft solid even further, thereby moving it closer to its physical gel point. For clay/sPB, the shear-induced changes were irreversible so that they could get probed using small amplitude shear (SAOS) frequency sweeps. Sequences of SAOS-LAOS-SAOS (SLS) where repeated with increasing LAOS amplitude and increasing duration. The flow-induced structural changes in the soft solid were attributed to yielding, which began to occur at about the same stress/strain values as found for the onset of nonlinearity in traditional SAOS to LAOS (StL) stress amplitude sweeps. The onset of nonlinearity and the yielding seem to be a strain activated process since the characteristic strain amplitude is independent of frequency and temperature, but not so for the characteristic stress amplitude. The duration of LAOS in a SLS experiment beyond yielding is an important parameter since flow-induced structural changes require time to grow.