The phrase "crosses threshold" implies a sense of progression or advancement, but its antonyms suggest a lack of movement or regression. Words that are antonyms for this phrase include stagnates, regresses, retreats, or declines. These words convey a sense of inertia or retreat instead of progress. Stagnates indicates a lack of development or growth, whereas regress and retreats indicate a decline from a previously attained level. Decline can imply a decrease in quality, prestige, or importance. So, if you want to convey an opposite sense to "crosses threshold," these are some of the appropriate antonyms you can use.