If you can get back to finishing it within the following day and a half, treating the unsmoked portion right will allow you to relight without losing much enjoyment.
1. Before the cigar burns itself out, purge the smoke by blowing through the cut until the body is emptied of residual smoke that, if allowed to remain in there, could sour the filler and/or binder.
2 Let the cigar extinguish naturally.
3. After tapping off the end ash, use a toothpick or some other tool to scrape any leftover loose, white ash off the foot.
4. Wrap all but the blackened foot (leave that exposed to the air) in plastic wrap and store in a properly humid area that you don't care picks up the aroma of a leftover cigar.
The blackened foot as a plug and plastic wrap (I have even stored the wrapped butt in a toothpaste box too for extra insulation, again leaving the foot outside the box so that end does not contaminate the body) will tend to insulate and keep the tobacco fresh for about another 36 hours, depending on the location it is stored. When you light it back up, it may take 3/4 inch of smoking to get back to that original fresh tobacco in order to enjoy the gar's aroma and taste, but it can happen.