The most common and most likely answer to this crossword clue is the 7 letter word MOULDER
I've seen this crossword clue in The Sunday Telegraph
M
O
U
L
D
E
R
Buddy explains!

The straight part
We know that "begin to crumble" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case begin to crumble = moulder.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 MOULDER mean?
MOULDER noun- A person who moulds dough into loaves.
- Anyone who moulds or shapes things.
- A machine used for moulding.
- To decay or rot.