The most common and most likely answer to this crossword clue is the 6 letter word ELOPES
I've seen this crossword clue in The Times
E
L
O
P
E
S
Buddy explains!

The straight part
We know that "runs off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case runs off = elopes.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 ELOPES mean?
ELOPES verb- (of a married person) To run away from home with a paramour.
- (of an unmarried person) To run away secretly for the purpose of getting married with one's intended spouse; to marry in a quick or private fashion, especially without a public period of engagement.
- To run away from home (for any reason).