The most common and most likely answer to this crossword clue is the 7 letter word UNOWNED
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More clues leading to the result UNOWNED
Buddy explains!

The straight part
We know that "Nobody’s" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nobody’s = unowned.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 UNOWNED mean?
UNOWNED adjective- Not owned; not having an owner.
- Not avowed or acknowledged as one's own property or one's own work.