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Question

When do you use an object pronoun in the subject position of a sentence? For example "us students need to study hard".

Thank you for your prompt help.

Answer 1

Never, ever.  "We students need to study hard" is correct.  (If you use "us students need to study hard" it only illustrates, that, yes, you do need to study!)

Answer 2

Anytime in the beginning (but not always) of a sentence before the subject. Its a way of making clear which students you're talking about.