The phrase "runs the risk" typically refers to the possibility of experiencing negative consequences if a particular action is taken. There are numerous synonyms that can be used to express the same idea, including "takes a chance," "puts oneself in jeopardy," "faces peril," "courts disaster," "tempt fate," "risks harm," and "exposes oneself to danger." Other options might include "invites trouble," "embraces uncertainty," or "dares to engage." Regardless of the phrasing used, the common thread is that there is a clear recognition of the potential risks involved in a given course of action and a willingness to proceed despite them.