To be out of options or alternative courses of action; to be stuck in a bad situation.
A 'rope' is thrown to someone who is in a difficult place, such as deep water or the edge of a cliff. If there is not enough rope, the person might be in trouble. So to be 'at the end of your rope' means that there is no more help available, and the situation is not good.
Synonyms: in a jam, at wit's end
I'm at the end of my rope -- I lost my job, my car died, and I don't have any money in the bank.
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