Green’s Dictionary of Slang

duck n.7

also ducks, doup

(US) a cigarette or cigar end; thus shoot ducks, to relight a cigar or cigarette end.

[US]L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:iv 308: duck, n. A cigarette stub.
[UK]K. Mackenzie Living Rough 175: Where’s that doup (cigarette butt) I left on the mantlepiece.
[US] ‘Citadel Gloss.’ in AS XIV:1 Feb. 26/2: duck, n. A partially consumed cigarette.
[US]T.J. Farr ‘The Language of the Tennessee Mountain Regions’ in AS XIV:2 90: ducks. A lighted cigarette stub.
[US]Wentworth & Flexner DAS.

In compounds

duck buddy (n.) (also duck buddie) [buddy n. (2)]

(US) one who, bereft of a cigarette himself, is given the last few puffs on a friend’s.

W.H. Amerine Alabama’s Own 303: Brownie and me are ‘Duck Buddies,’ have been from the first. Don’t know what a ‘Duck Buddie’ is? Well, you see, if a man has some ‘makin’s’ and his buddie hasn’t, the buddie always gets the ‘ducks’ – the last half inch or so of the cigarette, I mean [HDAS].