The most common and most likely answer to this crossword clue is the 6 letter word MOULDY
I've seen this crossword clue in The Daily Telegraph
M
O
U
L
D
Y
More clues leading to the result MOULDY
Buddy explains!

The straight part
We know that "going off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case going off = mouldy.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 MOULDY mean?
MOULDY adjective- Covered with mould.
- Neglected.
- Worthless; lousy; rotten