The most common and most likely answer to this crossword clue is the 10 letter word UNATTACHED
I've seen this crossword clue in The Guardian
U
N
A
T
T
A
C
H
E
D
More clues leading to the result UNATTACHED
- Sort of case in German and it's not fixed
- Novelty act had tune for single
- Cut any tax, attack the reds without borders and without strings
- Single aunt hated Dicky without a hint of contrition
- A hunt acted badly on its own
- Single girl longed to possess Otto’s heart
- A neat Dutch organisation is independent
- Heat and cut in pieces on your own
- Disturbingly cute, at hand — and without ties
- Loose definition would be ‘fancy-free’
Buddy explains!

The straight part
We know that "on its own" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on its own = unattached.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 UNATTACHED mean?
UNATTACHED adjective- Not attached or joined; disconnected.
- Not married or involved in a romantic relationship.
- Not connected with or belonging to a particular group or organization.
- Not seized for debt.