I'm a bit confused about how "しかい" is used in this sentence I came across while studying:
そこには私一人しかいなかった。 "I was the only one there."
My guess is that it is an ending to "一人", but I couldn't find any information supporting that.
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It's actually the particle
しか "nothing but/nobody but" plus
いなかった, the negative past form of
いる "to be/to exist" (animate). Your translation is right. It means "I was the only one there".
しか is always paired with negative verbs like this. Taking an example from A Dictionary of Basic Japanese Grammar (p.401):
Nobody but Bob came. = Only Bob came.
しか works the same way in your example.