The saying "hanging on by a thread" refers to a situation of extreme fragility or vulnerability, where something is barely holding together and on the verge of collapse or failure. It conveys the idea that only a very small or tenuous connection is keeping a person, plan, or circumstance from falling apart. This phrase is often used to describe moments of emotional, physical, or situational strain where stability is precarious, and even a minor disruption could cause everything to unravel.