To be 'hanging by a thread' means to be in a dangerous or precarious position or to be very close to failure or a serious outcome. If you are 'hanging by a thread' any change to your circumstance could have a dramatic impact on your welfare or prognosis. Similar in meaning to being 'on thin ice'.

1. After he was hit by a car, Gary was taken to hospital where his life hung by a thread for a while before making a miraculous recovery.
2. We managed to hang on to our house by a thread by working two jobs each and cutting our spending.

1. Being rude to that customer was a big mistake. Her job was already hanging by a thread before this incident so I'd say she will definitely be fired now.
2. The chances of us completing this deal may hang by a thread after the breakdown of talks, but there is still some hope it can be salvaged.