Observations show that the near-sill dynamics of dense abyssal overflows is variable and is governed, to a significant extent, by a balance between rotation, bottom friction and downslope acceleration due to gravity. Numerical simulations indicate that the near-sill downslope velocities are comparable to the phase/group velocities of long internal gravity waves. This suggests the possibility that overflows can become supercritical and destabilized by bottom friction. A theory is presented for the frictional destabilization of rotating abyssal overflows and the accompanying baroclinic coupling with the overlying ocean. This mode of transition allows for the formation of downslope and alongslope propagating periodic bores or pulses in the overflow and the generation of amplifying long internal gravity waves in the overlying ocean, and may help to explain aspects of the observed variability which seem unrelated to purely inertial baroclinic instability.