The most common and most likely answer to this crossword clue is the 13 letter word DISINTEGRATES
I've seen this crossword clue in The Times
D
I
S
I
N
T
E
G
R
A
T
E
S
Buddy explains!

The straight part
We know that "decays" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case decays = disintegrates.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 DISINTEGRATES mean?
DISINTEGRATES verb- To undo the integrity of, break into parts.
- To fall apart, break up into parts.