relight
Originating in Northern California, a relight is a cigarette butt found on the ground or in an ashtray. The finder of the relight hopes the person who smoked the cigarette before them doesn't smoke a lot of the cigarette so there is still tobacco left in it for them to use.
"Aye Jack can i bum a cig off u im really craving one"

"Nah Cy, just pick up a relight I saw tons on the street behind us"