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

The straight part
We know that "Fallen" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fallen = lapsed.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 LAPSED mean?
LAPSED verb- To fall away gradually; to subside.
- To fall into error or heresy.
- To slip into a bad habit that one is trying to avoid.
- To become void.
- To fall or pass from one proprietor to another, or from the original destination, by the omission, negligence, or failure of somebody, such as a patron or legatee.
- Discontinued; having ceased or gone out of use.
- (of a person) Changed to a less valued condition or state; especially having lost one's religious faith.
- By extension, having changed a (secular) belief or adherence.
- (of a legacy) Having passed from the original holder or authority; no longer claimed.