As we've been discussing, there are some (primarily resistive) loads which are incredibly unlikley to develop in an 'overload' current, although any can, of course, give rise to a 'fault' current (i.e. due to some sort of 'short-circuit'.Any electrical item can go faulty and and as a the result of that fault draw more than it's design current, some items have fault protection in the form of a fuse internal to the item.
The 'nightmare' faults (the the everyday, not technical, sense) are those which are of low, but not 'negligible' impedance, since there's really no way we can, at least at present, realistically protect against them with over-current devices. One would need devices that had much lower 'magnetic trip thresholds' than our current ones - but that would then probably result in a lot of 'nuisance' tripping (since the thermal part of present-day OPDs is pretty tolerant to relatively short-term 'overload' currents).
Kind Regards, John