The most common and most likely answer to this crossword clue is the 9 letter word FRANGIBLE
I've seen this crossword clue in The Guardian
F
R
A
N
G
I
B
L
E
More clues leading to the result FRANGIBLE
Buddy explains!

The straight part
We know that "Dainty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dainty = frangible.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 FRANGIBLE mean?
FRANGIBLE noun- Something that is breakable or fragile; especially something that is intentionally made so, such as a bullet.
- Able to be broken; breakable, fragile.