noun which may take the genitive case particle 'no'
half-smoked; partially smoked
Describes a cigarette or similar item that has been lit and partially consumed but not finished. Often used as a noun modifier with の.
灰皿に吸いかけのタバコが何本もあった。
There were several half-smoked cigarettes in the ashtray.
吸い殻 refers to a cigarette butt or the remaining filter after smoking, while 吸いかけ emphasizes that the cigarette is only partially smoked and still has usable tobacco left.
Compound of 吸い (stem of 吸う 'to smoke') + かけ (from 掛ける, indicating an action left incomplete).