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The concept is known as abdication. In some cases of history, leaders of a monarchy have been "allowed", or in reality coerced to give up the throne to a family member.
Since you specifically brought up Tsar Nicolas II, we can definitely say no. He attempted first to abdicate to his son, then quickly to another family member Grand Duke Michael Aleksandrovich.
The new government at the time was known as the Provisional government and did not accept this. But more importantly, this was essentially the beginning of the Russian Civil War. No party ever endorsed the Grand Duke and it was not until the end of the Russian Civil War that one party established power in Russia.
Reference material:
https://en.wikipedia.org/wiki/Grand_Duke_Michael_Alexandrovich_of_Russia#Abdication_of_Nicholas_II