In the active sentence, «الدَّرْسَ» is the accusative object. After passivization it occupies the nominative passive-subject position as «الدَّرْسُ».
The case change reflects the changed syntactic relationship. The lesson is still what was written; it has not become the writer.
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Mafʿūl Mā Lam Yusamma Fāʿiluhu — The Passive Subject
In the active sentence, «الدَّرْسَ» is the accusative object. After passivization it occupies the nominative passive-subject position as «الدَّرْسُ».
The case change reflects the changed syntactic relationship. The lesson is still what was written; it has not become the writer.