Grant,
I have been thinking about my answer for a while and I am going to add to it!
If a 6v radio is run from a 12v supply using a correctly chosen resistor value, the radio will perform normally. If then one of the filaments burns out, the radio will stop working, which is normal. What will happen though is that the voltage to the radio will go up some because less current is passing through the resistor. If the radio was continually left on, it is conceivable that another filament could blow and of course the voltage would go up again. Ultimately, leaving a nonfunctioning radio turned on while powered through a dropping resistor could eventually result in a radio being fed with a voltage close to 12v.
This whole scenario could be avoided by using a solid state regulated supply which delivers the same voltage constantly.
