Green’s Dictionary of Slang

curbstone n.

also kerbstone

(US tramp) a cigarette made from the remains of extinguished cigarettes dropped in the gutter.

[US]N. Klein ‘Hobo Lingo’ in AS I:12 650: Curbstones — cigar or cigaret ends.
[US]Irwin Amer. Tramp and Und. Sl. 58: Curbstones. – Cigar and cigarette ends picked up on the street or in the gutter.
[US]Wentworth & Flexner DAS.