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to be (of animate objects); to exist
to stay
to be ...-ing
to have ...-ed; to be ...-ed
「居る」 has another reading with different meanings.
猫が窓辺に居るのが見えた。
I could see the cat by the window.
そこに居てくださいね。
Please stay there, okay?
昨日はずっと家に居たよ。
I was at home all day yesterday.