In the sentence
Watashi no hon.
Can the owner be omitted?
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One minor exception would be “finishing someone else’s sentence”, like
“ Who did it? Taro?”
“...’s little brother, actually.”
But this is really only possible when the last word of the person you are speaking to is the head of your sentence. It feels less like a grammatical thing and more like a conversational trick.
The short answer is no.
While you can leave off the subject of a sentence if it is understood, the same cannot be done this grammatical structure.
の is a particle that is formed by the following structures
Noun の Noun
(watashi no hon)
Noun (particle) の Noun
(Amerika kara no hon).
Often, you will see it in connection with noun phrases, which makes the usage very versatile, but not in the way you ask.