The phrase "are on the edge" indicates that someone or something is in a precarious position or situation. There are several synonyms that can be used to convey this idea, such as "are at risk," "are teetering on the brink," "are on the verge," "are in danger," "are hanging by a thread," "are walking a tightrope," "are poised for disaster," "are in a critical state," and "are skating on thin ice." All of these synonyms convey a sense of imminent danger or potential downfall. Using these alternatives can add variety and nuance to your language, while still effectively conveying the idea of a precarious situation.