You won't mind a "yes and no" answer, will you?
If by fragment, you mean something that one might actually say,
expecting to be understood, then no, it doesn't have to be part of a
fully expressed sentence.
If you mean the speaker expects to hearer to understand what a complete
sentence built on that fragment would mean in the context, then yes, it
has to lead to the understanding of a proposition.
Probably a stilted example, but,
きみ、こんな本読む?
いや、ぼくは...
And maybe that's not what your question was supposed to mean.
Bart
Rereading to see whether I was answering your question, I became more
aware of the above. My example didn't have a modified noun in it (but of
course I could have made it いやあ、そんな本は...).
If Jorden's "fragments" are just examples of modifiers and nouns, not
utterances (no periods), then there is no more or less reason why there
couldn't be a -wa after the noun than a -wo, -ga, -kara, -da, or
whatever. It sounds like she is giving examples of things that could be
in sentences.
Bart again.
Sorry, I hadn't attached enough weight to the "in" of "... 'wa' cannot
be used in a fragment."
Now that I see you mean that "hanako-wa tabeta sashimi" could not be a
fragment (in the special sense of the word), I say you are quite correct.
Can you translate this whole message into Japanese, please?
I can understand in Japanese better because Japanese is my mother
tongue like your mother.