The most common and most likely answer to this crossword clue is the 9 letter word DESCENDED
I've seen this crossword clue in The Times
D
E
S
C
E
N
D
E
D
Buddy explains!

The straight part
We know that "went downhill" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went downhill = descended.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 DESCENDED mean?
DESCENDED verb- To pass from a higher to a lower place; to move downwards; to come or go down in any way, for example by falling, flowing, walking, climbing etc.
- To enter mentally; to retire.
- (with on or upon) To make an attack, or incursion, as if from a vantage ground; to come suddenly and with violence.
- To come down to a lower, less fortunate, humbler, less virtuous, or worse, state or rank; to lower or abase oneself
- To pass from the more general or important to the specific or less important matters to be considered.
- To come down, as from a source, original, or stock
- To be derived (from)
- To proceed by generation or by transmission; to happen by inheritance.
- To move toward the south, or to the southward.
- To fall in pitch; to pass from a higher to a lower tone.
- To go down upon or along; to pass from a higher to a lower part of