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The dying days of Britain's rule in Palestine were marked by destruction, blood, and the start of the Palestinian exile, meaning the expulsion of the majority of the Palestinian people against the backdrop of Zionist terrorism.
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Republicans have made the killing of four Americans at the US consulate in Benghazi, Libya, a central theme in the dying days of their campaign.
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Does the dying days mean the last days?
I prefer the OP's 'rule' context rather than the 'campaign' one though. The campaign will end just because it ends, not because of any violence or infirmity or what-have-you. I like my 'dying days' to refer to the death of something, rather than just its end. Not all English speakers share this faddiness though.