The phrase "ceased to exist" has a finality to it. It implies something has come to an end, and will no longer continue. There are many synonyms for this phrase, such as "perished," "expired," "passed away," "gone," "departed," "vanished," "disappeared," "ended," "terminated," "died out," "extinct," "disintegrated," "disappeared," and "withered away." Each of these words carries a slightly different connotation, but all express the same idea of something no longer existing, whether it is a person, thing, or concept. Using these synonyms can add variety and depth to your writing.