Relighting a Cigar
The short answer is: Yes. A cigar can be relit and it would be a waste of money to toss half of a gourmet cigar away simply because one needed to extinguish it before they were finished smoking. However, there will be some impact on the taste of the cigar when it is relit. Some individuals find this change in taste objectionable while others either do not notice or even prefer the taste of a relit cigar.
As tar builds up in the tobacco during the smoking process, the flavor of the cigar inevitably changes. This change in and of itself is not necessarily unpleasant. In fact, some cigar smokers enjoy the flavor of a half to almost completely smoked cigar to a fresh one. The effect can seem more pronounced when a cigar is put out and relit, however.
Some butane torch lighters come with a cutting attachment. Snipping off the ash and exposing the wrapper allows one to relight the cigar just as they would light a fresh cigar. If one wishes to preserve the maximum amount of tobacco, one can simply knock off what ash remains at the foot of the cigar and relight at that spot. This may result in a somewhat harsher taste, especially on the first few draws.
If the cigar is trimmed back, there will likely be some darkening of the tobacco, particularly in the center of the cigar where the smoke tends to be drawn through the most. This is nothing to worry about and the tobacco will still taste good. In fact, some smokers actually prefer this taste as it has a bit more "bite" to it and offers a different smoking experience.
Good cigars can be expensive and, given that they're large, many smokers actually prefer to smoke them in stages. Generally, the more times a cigar is relit the harsher it will become so most smokers prefer to limit this to one relight per cigar. With a very good cigar, however, the quality of the smoke may well make multiple relights completely acceptable.