The most common and most likely answer to this crossword clue is the 8 plus 4 letter word TWILIGHT ZONE
I've seen this crossword clue in The Guardian
T
W
I
L
I
G
H
T
Z
O
N
E
Buddy explains!
The straight part
We know that "a run-down area" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a run-down area = twilight zone.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.