The most common and most likely answer to this crossword clue is the 11 letter word MELANCHOLIA
I've seen this crossword clue in The Sunday Telegraph
M
E
L
A
N
C
H
O
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A
More clues leading to the result MELANCHOLIA
Buddy explains!

The straight part
We know that "depressed state" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case depressed state = melancholia.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.
Crossword Answer definitions
MELANCHOLIA noun- Deep sadness or gloom; melancholy.
- Clinical depression, characterised by irrational fears, guilt and apathy.