"Hangs by a thread" is an idiomatic expression used to describe a precarious situation or something that is in a state of uncertainty or danger. Antonyms for this expression could include "secure," "stable," "steady," and "firmly established." These words suggest a sense of safety, certainty, and reliability, which are the opposite of the fragility and instability that are implied by "hangs by a thread." Other possible antonyms could include "strong," "durable," "resilient," and "robust," which denote a sense of strength and durability. In any case, the antonyms of "hangs by a thread" convey a sense of confidence and reassurance, which are the opposite of the uncertainty and anxiety that are associated with this expression.