Ceases to exist is a phrase used to describe when something no longer exists. Synonyms for this phrase include disappears, vanishes, fades away, terminates, ends, and dissolves. Another alternative is to use the word 'extinguish', which can imply a sudden end or a final act that marked the end of something. Additional synonyms may include the phrases 'runs out', 'disappears into thin air', 'passes away', or 'evaporates.' The choice of words depends on the context of the sentence and the tone of the speaker. However, all of these synonyms convey the same meaning that something has ceased or has been ended.