We discuss the flux and polarization signals obtained from the microlensing of stars with extended circumstellar envelopes by a single point-mass lens. A previous paper considered the case of main-sequence stars, and showed that microlensing of the stellar photosphere could produce a small net polarization (up to 0.1 per cent). In this paper, we show that stars with extensive envelopes will show a much higher level of variable polarization (up to 10 per cent), even if they are spherically symmetric. Since the stellar envelopes most likely to be lensed are produced by red giant winds, we also investigate the effects of a central cavity (representing the dust condensation radius) within the scattering envelope, as well as different radial density distributions. Our study has led to three major results. (i) For optically thin envelopes with an inner cavity, the lensing light curve for the polarization can be of longer duration than that for the total flux, the latter being dominated by the much brighter, unpolarized photospheric emission. If observed, the differing time-scales would provide direct evidence of a thin circumstellar envelope with a cavity. (ii) The combination of photometric and polarimetric light curves determines the lens impact parameter even if the event is not a photospheric transit. (iii) The variation of the polarization position angle determines both the magnitude and direction of the relative proper motion. Finally, we derive an asymptotic limit of the lensing polarization for large Einstein radii. This limit greatly simplifies the determination of the lensing parameters.