A successful unified description of $\bar p$ nuclear interactions near E=0 isachieved using a $\bar p$ optical potential within a folding model, $V_{{\rmopt}} \sim \bar v * {\rho}$, where a $\bar p p$ potential $\bar v$ is foldedwith the nuclear density $\rho$. The potential $\bar v$ fits very well themeasured $\bar p p$ annihilation cross sections at low energies ($p_L < 200$MeV/c) and the $1s$ and $2p$ spin-averaged level shifts and widths for the$\bar p$H atom. The density-folded optical potential $V_{{\rm opt}}$ reproducessatisfactorily the strong-interaction level shifts and widths over the entireperiodic table, for $A > 10$, as well as the few low energy $\bar p$annihilation cross sections measured on Ne. Both $\bar v$ and $V_{{\rm opt}}$are found to be highly absorptive, which leads to a saturation of reactioncross sections in hydrogen and on nuclei. Predictions are made for $\bar p$annihilation cross sections over the entire periodic table at these very lowenergies and the systematics of the calculated cross sections as function of$A$, $Z$ and $E$ is discussed and explained in terms of a Coulomb-modifiedstrong-absorption model. Finally, optical potentials which fit simultaneouslylow-energy $\bar p - ^4$He observables for $E < 0$ as well as for $E > 0$ areused to assess the reliability of extracting Coulomb modified $\bar p$ nuclearscattering lengths directly from the data. The relationship between differentkinds of scattering lengths is discussed and previously published systematicsof the $\bar p$ nuclear scattering lengths is updated.
