We refer on some recent studies on classical electrodynamics of point particles, as described by the Abraham-Lorentz-Dirac equation. Such studies exploit positively the well known existence of generic runaway solutions. Indeed the additional requirement that has to be imposed, namely the restriction to initial data giving rise to nonrunaway behaviour, turns out to allow for unexpected phenomena, for example a behaviour qualitatively similar to that occurring in the quantum tunnel effect. It is pointed out how this fact might be relevant for the problem of hidden parameters.