جَاءَ أَبٌ — A father came: abun is a nominative subject with tanwīn.
جَاءَ أَبِي — My father came: abī is a nominative subject with possessive iḍāfah and an estimated ending.
Iḍāfah changes the form but not its grammatical role as subject.
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Abun versus Abī
Iḍāfah to Yāʾ al-Mutakallim and the Six Nouns
جَاءَ أَبٌ — A father came: abun is a nominative subject with tanwīn.
جَاءَ أَبِي — My father came: abī is a nominative subject with possessive iḍāfah and an estimated ending.
Iḍāfah changes the form but not its grammatical role as subject.