We report on a set of clear and abrupt decreases in the high‐frequency boundary of whistler mode emissions detected by Cassini at high latitudes (about ±40°) during the low‐altitude proximal flybys of Saturn. These abrupt decreases or dropouts have start and stop locations that correspond to L shells at the edges of the A and B rings. Langmuir probe measurements can confirm, in some cases, that the abrupt decrease in the high‐frequency whistler mode boundary is associated with a corresponding abrupt electron density dropout over evacuated field lines connected to the A and B rings. Wideband data also reveal electron plasma oscillations and whistler mode cutoffs consistent with a low‐density plasma in the region. The observation of the electron density dropout along ring‐connecting field lines suggests that strong ambipolar forces are operating, drawing cold ionospheric ions outward to fill the flux tubes. There is an analog with the refilling of flux tubes in the terrestrial plasmasphere. We suggest that the ring‐connected electron density dropouts observed between 1.1 and 1.3 R s are connected to the low‐density ring plasma cavity observed overtop the A and B rings during the 2004 Saturn orbital insertion pass.