"Cease to exist" is a popular use of the word cease, or end, and you may have closed your eyes and wished that someone — the boogeyman in the dark or a pesky sibling by day — would stop! Go away! Cease to be! Or, at the very least — quit bugging you.
A French word from 1300, cesser, meaning "come to an end," "go away," "give up," and "yield" is the root of cease. Although cease often appears in the past tense with "-ed," cease is common for talking about things as they come to an end. A dead plant has ceased living, and if you cease watering the rest of the plants, they will cease to exist too.