We report the \textit{ab initio} prediction of a negative Barkas coefficient in LiF insulator at low velocity (v< 0.25 a.u. ~ 2 keV). The electronic stopping power of protons in lithium fluoride has been extensively studied both experimentally and theoretically because of a controversial threshold effect. While our time-dependent density-functional theory (TDDFT) simulations confirm the presence of a velocity threshold below which the proton stopping power vanishes, our calculations demonstrate that the antiprotons do not experience such a threshold. The combination of those two contrasting behaviors gives rise to an unprecedented negative Barkas effect: the stopping power of antiprotons is larger than that of protons. We identify that the slow antiproton at close encounter destabilizes a p orbital of the F- anion pointing towards the antiproton. This particular orbital becomes highly polarizable and hence contributes much to the stopping power.