The most common and most likely answer to this crossword clue is the 9 letter word LAST-GASP
I've seen this crossword clue in Independent
L
A
S
T
-
G
A
S
P
More clues leading to the result LAST-GASP
Buddy explains!

The straight part
We know that "Absolutely final" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case absolutely final = last-gasp.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does LAST-GASP mean?
LAST-GASP adjective- Happening at the very end of an event.