Can I make the word "noun" into a generic with the definite article ?
The noun can be a subject or object.
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A noun can function as a subject or object.
Here 'a' does the job you were looking for. You could also say 'Nouns can function...'
If you say 'the noun', that means you have a particular noun in mind - 'giraffe' for instance.
Edit: There are cases where generic noun phrases can be made with 'the' but here it sounds strange and is ambiguous.