This can happen whether there is current being drawn by the plugged-in devices. All it takes is a slight breakdown of insulation and a resultant small arc. A small arc heats the insulation and breaks it down even more. etc etc. The key here is that the circuit breakers that you (and I and most everyone else) have is not built to trip on an arc -- it requires a substantial current overload to do its job but an arc does not necessarily draw a lot of current while it does generate a lot of localized heat.
In some building codes the newer arc-fault circuit breakers that will protect in this sort of situation as well as current overload are required, sometimes everywhere and sometimes only in bedrooms, but there is no requirement AFAIK to retrofit.