The most common and most likely answer to this crossword clue is the 11 letter word VALEDICTION
I've seen this crossword clue in The Guardian
V
A
L
E
D
I
C
T
I
O
N
Buddy explains!

The straight part
We know that "Farewell" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case farewell = valediction.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 VALEDICTION mean?
VALEDICTION noun- A speech made when leaving or parting company.
- The act of parting company.
- A word or phrase (such as adieu or farewell) said upon leaving.
- A word or phrase used to end a letter or message.