Green’s Dictionary of Slang

doss n.2

[? link to Scot. doss, a tobacco-pouch]

(UK juv.) the last few puffs of a cigarette.

OnLine Dict. of Playground Sl. 🌐 doss n. [...] (3) The end of a cigarette that has been smoked, usu. by an older or richer boy or girl. ‘save us a doss’.