The idiom at the end of one's rope means that a limit has been reached, that there can be no progress or movement forward that the end is now here. A rope is used as a safety device, as well as to execute someone by hanging. The end of a rope is not a good place to be in either case.
Example 1: After the terrible events of the year and the breakup of the company, John felt hopeless, that he was at the end of his rope.
Example 2: If you are at the end of your rope, I think that getting therapy and support from professionals is a good idea.
Example 3: Sometimes when you get to the end of your rope, the desperation is stimulating and helps you solve your problems out of necessity.
Example 4: Sheila is really at the end of her rope - she lost her job, her husband, and her house, and she has no choice but to start over.