Marian had plenty of work to finish
In the correction form, it says that the function of to finish is adverbial.
But why it is not an adjective? Which work? The work to finish. So it is an adjective!!
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Marian had plenty of work [to finish].
The bracketed element is neither an adjective nor an adverb, but an infinitival relative clause modifying "plenty of work".
It has a modal meaning comparable to that expressed in finites by "can" or "should", and is thus comparable to Marian had plenty of work that she could / should finish.
Note that 'adjective' and 'adverb' are parts of speech, not clause types.