The most common and most likely answer to this crossword clue is the 10 letter word MOTH-EATEN
I've seen this crossword clue in The Times
M
O
T
H
-
E
A
T
E
N
More clues leading to the result MOTH-EATEN
- Decrepit bully gives up resistance after shake
- Old men will keep turning to passion
- Old article in complex meant to be shabby
- Antiquated test hard at elite school, they say
- Looking shabby, he meant to reform
- Mum mostly had name that is old-fashioned
- Shabby mat, the one that's dirty
- Untidy at home, 10 becomes shabby
- Woman in Missouri shelter mostly the worse for wear
- Shabby way of working not right to challenge
Buddy explains!

The straight part
We know that "shabby" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shabby = moth-eaten.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 MOTH-EATEN mean?
MOTH-EATEN adjective- Containing holes by having been eaten by moth larvae.
- Old and in poor condition