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We present polarimetric and spectroscopic observations of the X-ray binary A0538-66 obtained in 1991 near periastron passage during cycles 291, 294, and 310. The system was in an active phase during cycle 291 (φ=0.98), with X-ray outbursts being observed in the previous two cycles. By cycle 294 (φ=0.00-0.12) the system had entered a low-activity phase, and by cycle 310 (φ=0.06) the system appears to be fully ``off.'' We address the implications of these new observations and interpret them within the context of the model put forward by Clayton et al. in which the polarization arises from scattering of the B2 IIIe star's light from circumstellar disk material as well as additional material in the orbital plane. The rapid change in position angle near periastron passage, observed in the previous polarimetric studies and ascribed to additional scattering material in the Clayton et al. model, is not seen in our postoutburst observation. We suggest that the absence of additional scatterers may be associated with the transition from the ``on'' to the ``off'' state that took place in 1991.