at stake and being on the line both that similar references. to have a lot a risk or to have a lot to lose. hanging by a thread refers more to a situation you might be in. but all phrases have to do with risk.

He didn’t work hard at his job, so it could be at stake. He didn’t work hard at his job, so it could be on the line. ‘Be at stake’ and ‘Be on the line’ both have the same meaning in this context - He could lose his job - something that might be valuable to him - meaning it is very possible at this point that this could happen. ‘Be on the line’ could possibly mean that there is a greater risk of this happening. He didn’t work hard at his job, so his chances of keeping it are hanging by a thread. However, ‘hang by a thread’ in this context means it is extremely probable that he will lose his job. The damage is done and there is very little he can do at this point to fix it.