This is a question I get a lot, one that can also send a shiver down the spine of any well-seasoned cigar aficionado...
Let's answer the YES side of the equation
If you are actively smoking a cigar and it goes out, then YES;
- Purge stale smoke - gently blow back through your cigar to remove any stale smoke
- Brush/gentle tap-off the ash
- Toast the foot with a soft-flame lighter, cedar spill or match and relight
- Alternatively use a butane-torch and angel it and then relight your cigar by holding the cigar just out of the butane flame and gently rotate and puff until relit
- Take slow puffs, gently bring it back to life
- Don't forget to let the cigar rest between puffs, but not so long as that it goes out again
- If not, then gently use your butane lighter on an angel and keep the cigar just out of the direct flame and relight your cigar that way.
It is generally considered a bad idea to relight a cigar with copious amounts of ash remaining on the end, as you will just accentuate the potential ashy-taste you may get.
Now, when should you NOT relight a cigar
Should you put your cigar down for several hours (or heaven forbid overnight!) and then want to relight it, STOP!
My personal rule of thumb is I can relight a cigar after a meal, any longer than that; I'll just smoke the cigar with my meal and not risk it.
Why? When a cigar has been lit and even smoked for just a short amount of time; you have during the process of smoking it dragged/pulled cigar smoke through the leafy confines of your cigar; additionally when a cigar cools down any tar or moisture sticks (or stays put) and this is always going to leave bitter, ashy notes to what is left of a once fine cigar.
Worthy Note: Just like re-lighting a stale cigar is a big NO NO so is putting a half-smoked cigar back in your cigar storage. You will instantly introduce the foul acrid smell and taste of a half-smoked, ashy, tarry cigar to the other fine cigars in your collection.
What to do with that irresistible nub?
Well, if you are like me - you just smoke that nub down till there's about 3mm of cigar left (yes, I have asbestos fingers it seems - or maybe after a few thousand cigars I've dulled the nerves just perfectly).
One option is to use a Cigar Nubber or Poker tool to finish the cigar off.
Another option is to use a Corn Cob Smoking Pipe and wedge it in and finish it off that way.
Just be careful you don't burn your lips and/or drop it - they have a habit of hiding under sofa's and making nice burn holes in the carpet!