The most common and most likely answer to this crossword clue is the 4 plus 2 plus 4 plus 5 letter word FALL ON HARD TIMES
I've seen this crossword clue in The Daily Telegraph
F
A
L
L
O
N
H
A
R
D
T
I
M
E
S
More clues leading to the result FALL ON HARD TIMES
Buddy explains!

The straight part
We know that "Suffer poverty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suffer poverty = fall on hard times.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.