The most common and most likely answer to this crossword clue is the 5 plus 3 letter word LEAVE ONE
I've seen this crossword clue in The Times
L
E
A
V
E
O
N
E
Buddy explains!
The straight part
We know that "Neglect correspondence/abandon duty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case neglect correspondence/abandon duty = leave one.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.