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Let's take the sentence "Have they entered their password?", where we use "they" meaning "he/she", a third person of any or unknown gender. If we replace the pronoun "they" with a more specific noun, e.g. "the user" we'll also need to replace "Have" with "Has" — "Has the user entered the password?".
For some reason I'm thinking that there's a rule in English that say that pronouns can replace nouns without changing the structure of the sentence. Since using "they" as "he/she" is relatively new, does this mean that that old rule is no longer universal? Or is the sentence "Has they entered the password?" now grammatically correct?