The short remaining end of a cigarette

One word substitute is Stub.

Stump: the bottom part of a tree left projecting from the ground after most of the trunk has fallen or been cut down.
Stub: the truncated remnant of a pencil, cigarette, or similar-shaped object after use.
Rag: a piece of old cloth, especially one torn from a larger piece, used typically for cleaning things.
Scrap: a small piece or amount of something, especially one that is left over after the greater part has been used.