The (semantic) subject can only be in the accusative if the verb is in the infinitive.
Your subordinate clause has the personal verb form esset (as it should), and therefore the subject of the subordinate clause is in the nominative.
The subject is often left implicit, as it is often the same as the (semantic) subject of the governing ACI structure.
It is implicit here, too, but agreement with the explicit participle makes the case clear.
The reason I keep saying that the subject is semantic is that I don't consider it a full-fledged grammatical subject.
I would also never put a comma after scripsit, just as I would never separate the object from the predicate by a comma, but I may be misguided by Finnish (regarding both punctuation and whatever "lauseenvastike" is in English).
However, I acknowledge that this is just a point of view.
Unrelated to your actual query, I would find it more natural to replace eius quod with quid:
Quidam scripsit eam plane insciam, quid factura esset, venisse.
This would make quid factura esset an indirect question, which I find more natural here than a relative clause.
Caesar also seems to use the indirect question (De Bello Gallico, 7.77.1: inscii quid in Haeduis gereretur).
Also, I should remark that I'm not sure whether you could replace factura esset with faceret.