The most common and most likely answer to this crossword clue is the 5 plus 4 plus 5 letter word BURST INTO TEARS
I've seen this crossword clue in The Guardian
B
U
R
S
T
I
N
T
O
T
E
A
R
S
Buddy explains!
The straight part
We know that "Cry" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cry = burst into tears.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.