Hello, Rachel and Richard:
The man, rather nervous, opened the letter. [6a]
When it follows the subject, as in [6a], [the supplementive adjective clause] is in some respects like a nonrestrictive relative clause (cf 17.22ff):
The man, who was nervous, opened the letter.
But the adjective clause suggests that the man's nervousness is related to the content of the sentence, whereas the relative clause does not necessarily convey that implication.
Quirk, A Comprehensive Grammar of the English Language, p. 425
I'm not quite getting the bolded part. What could it be conveying instead?