When a capacitor is supplied with a voltage of a higher frequency than intended, what will happen? Does the capacitor 'overheat' or 'resonate'?
A destruction of the electrolytic capacitor (caused by over voltage or reverse polarity) may lead to fire or explosion that are not a good thing to happen during the flight. Who wants to enjoy the video, here. This is not always, as electrolytic capacitors often contain safety vents to prevent explosions. Also capacitors should be rated to higher voltage than is normally applied to them.
Even if the capacitor just short-circuits, depending on how it is wired it may be a risk of fire. This is especially true for capacitors wired between the two power rails in order to suppress electric interferences between multiple power consumers and provider. When the failed capacitor short-circuits the rails, normally a circuit breaker disconnects the power. There are safety capacitors for use if this danger is a concern.
I was not able to find any accident reports related specifically to the failed capacitors.