לרפואת אליענה רינה בת אלעזר יעקב
ונעמי בת טובה
ולזכות שושנה בת דבורה גיטל
The gemara [Brachos 53a] says that a candle that was kindled on Shabbos may not be used on Motzei Shabbos for havdala because an aveirh was done with it.
What if the candle was lit באונס? Rav Amiel [Middah 5] says that since we learn there that a candle that was kindled for a sick person MAY be used for havdala, we see that it is not the מעשה עבירה that prevents us from using the candle but the מעשה איסור. Kindling for a sick person MAY be a מעשה עבירה but it is not a מעשה איסור but a מעשה היתר.
In the same vein we must then say that if a candle was kindled באונס where there is no מעשה איסור [because it is not the person's fault that he lit the candle], even though there may be a מעשה עבירה since a candle was kindled on Shabbos - it is nevertheless permitted to be used for havdala.
But not so pashut [as pointed out in the מוסד הרב קוק edition].
Rashi [52b] says that one may not use a candle שלא שבת - that didn't rest, meaning that a Goy did melacha by the light of the candle. The Meiri learns that the Goy actually lit the candle.
Either way - we see that the problem here is not the מעשה איסור because it is not אסור for a Goy to perform melacha on Shabbos but the מעשה עבירה. That does not work with Rav Amiel's understanding that what prevents us from using the candle is the מעשה איסור but the מעשה עבירה doesn't bother us. Here we see that it is in fact the מעשה עבירה that is the problem.
We also see a "the velt tzittert" [the world shakes] "dike chidush" that when a Goy does a melacha on Shabbos it is called an aveirah.
If it weren't 2am, I would probably explain more:-).
ועוד חזון למועד!