The most common and most likely answer to this crossword clue is the 10 letter word LANGUISHED
I've seen this crossword clue in The Guardian
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More clues leading to the result LANGUISHED
Buddy explains!

The straight part
We know that "went into decline" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went into decline = languished.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 LANGUISHED mean?
LANGUISHED verb- To lose strength and become weak; to be in a state of weakness or sickness.
- To pine away in longing for something; to have low spirits, especially from lovesickness.
- To live in miserable or disheartening conditions.
- To be neglected; to make little progress, be unsuccessful.
- To make weak; to weaken, devastate.
- To affect a languid air, especially disingenuously.