The most common and most likely answer to this crossword clue is the 8 plus 5 letter word SOUTHERN FRIED
I've seen this crossword clue in The Guardian
S
O
U
T
H
E
R
N
F
R
I
E
D
Buddy explains!
The straight part
We know that "This hen wouldn’t want to be" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this hen wouldn’t want to be = southern fried.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.