The most common and most likely answer to this crossword clue is the 9 letter word SQUABBLED
I've seen this crossword clue in The Times
S
Q
U
A
B
B
L
E
D
More clues leading to the result SQUABBLED
Buddy explains!

The straight part
We know that "fell out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fell out = squabbled.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 SQUABBLED mean?
SQUABBLED verb- To participate in a minor fight or argument.
- To disarrange, so that the letters or lines stand awry and require readjustment.