Question:
So Chanukah is over and I am putting the menorah away (sigh). What should I do with the stubs of my candles, which were often blown out before fully burning down?
Answer:
Good question. What are you to do with the leftover oil or candle stubs? The issue at hand is that fuel set aside for the mitzvah of Chanukah lights is now considered sacred and should not be used for anything else.
But what did you actually "set aside"? Technically speaking, you fulfill the mitzvah of lighting the menorah once your lights have been burning for a half-hour after nightfall. Thus, the Code of Jewish Law1 tells us that whatever is left over from the oil that was to burn in that half hour—though the flame was somehow extinguished—is consecrated for the mitzvah and should be burnt after Chanukah to ensure that it is not used for mundane purposes. If, however, you filled your cups with so much oil or used such big candles that they burnt for longer than the required time and you still had leftover fuel, you are free to do whatever you want with those leftovers as they were never "set aside" for the mitzvah lighting.
Other authorities,2 however, maintain that any leftover fuel that was placed in your menorah should be treated as "set aside," and burnt. For this reason, it is customary to burn all the leftover wicks, oil or wax from your menorah after the holiday is finished.3
Obviously, this would not apply to the oil still in the bottle and the candles still in the box, which may be used in whichever manner you see fit.
Oil vs wood vs time Oil is simple. If you have liquid oil left, you can use it the next night of Chanukah. Or, if it is the last night, then you can use it the next year.
Candles are more complicated:
If you lit the menorah with the intention to let the candles burn completely, but then you have to go somewhere and can't leave them burning unattended, so you extinguish them, then they were set aside for a mitzvah, so you should not use them for something else. However, if enough of the candle is left for it to burn for another 30 minutes, then you can use it the next night of Chanukah. Or, if it is the last night, then you can use it the next year.
If you have a wooden menorah and need to blow out the candles to keep the menorah itself from burning, then you never intended for the entire candle to burn. Therefore, since you always had the intention not to burn the bottoms of the candles, there is no issue of the bottom being something that you set aside for a mitzvah or intended to burn.