The most common and most likely answer to this crossword clue is the 6 letter word ADIEUX
I've seen this crossword clue in The Times
A
D
I
E
U
X
More clues leading to the result ADIEUX
- Last messages for couple seen round India
- Last words from unclad ladies you kiss
- Last words of two people hugging one?
- Like a couple crossing island vales
- Goodbyes ending with a kiss
- Farewells from a Parisian couple hugging one
- Farewell words to the French about to meet death
- Depart, embraced by two from Australia, with kiss and goodbyes
Buddy explains!

The straight part
We know that "Last messages" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case last messages = adieux.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 ADIEUX mean?
ADIEUX noun- A farewell, a goodbye; especially a fond farewell, or a lasting or permanent farewell.