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The electronic excitations and the band structure determine the stopping power of the material and alter the interatomic forces for both channeling and off-channeling trajectories.   Our off-channeling results are in quantitative agreement with experiments, and at low velocity they unveil a crossover region of superlinear velocity dependence (with a power of $\sim 1.5$) in the velocity range $v = 0.07-0.3~\mathrm{a.u.}$, which we associate to the copper crystalline electronic band structure.  The results are rationalized by simple band models connecting two separate regimes.   We find that the limit of electronic stopping $v\to 0$ is not as simple as phenomenological models suggest and it plagued by band-structure effects. effects