A.  Actually, there are some cigar smokers who leave their unfinished cigars out over night, then continue smoking them the next day. (I read somewhere that Arnold Schwarzenegger used to do this with his cigars). Normally, the longer an unfinished cigar sits around, the more stale and even bitter-tasting it can become.

If, depending on the circumstances, you have no other choice but to return to your cigar later, my advice would be to clip the cigar back about a half-inch behind the foot to remove the ashen part and most of the tarry residue. This will at least give you a somewhat cleaner smoke when you relight. Just remember that the longer the cigar is left out, the more likely it will not taste as good as the first go-round, but some cigars may surprise you.