cessation
熄 centers on the idea of something coming to a complete stop or dying out, especially a fire or active process. The given meaning 'cessation' captures this sense of extinguishing or ending.
熄 combines 火 (fire) with 息 (breath/rest), suggesting a fire being put out or dying down. The exact historical development is uncertain, but the phono-semantic structure is plausible.
The fire radical 火 beside 息 (breath/rest) paints a picture of a flame being blown out or resting until it ceases. Imagine a candle flame extinguished by a gentle breath.
For ソク, picture a sock being used to smother a small flame: sock -> ソク, and the fire ceases.