What is the stand-in doer (nā'ib al-fā'il)?
Sometimes the doer is not mentioned at all — because it is unknown, or because the speaker has no reason to name it. The verb then changes its shape, and the word that would have been the object steps into the empty place.
Compare the two. ضَرَبَ عَمْرٌو زَيْدًا (ḍaraba 'amrun zaydan), 'Amr struck Zayd — زَيْدًا is the object, in nasab. Now drop the doer: ضُرِبَ زَيْدٌ (ḍuriba zaydun), Zayd was struck. The same word is now مَرْفُوع, because it is now filling the doer's role.
Name the doer and you have a fā'il with an object in nasab. Leave the doer unnamed and the object moves up into rafa as the nā'ib al-fā'il.
The verb marks the change on itself. In the past tense the first letter takes a ḍamma and the letter before the last takes a kasra — ضَرَبَ becomes ضُرِبَ. In the present tense the first letter takes a ḍamma and the letter before the last takes a fatḥa — يَضْرِبُ becomes يُضْرَبُ.
The older books name this role by describing it rather than titling it: اَلْمَفْعُولُ الَّذِي لَمْ يُسَمَّ فَاعِلُهُ, “the object whose doer has not been named”.
Like most Arabic grammar terms, نَائِب (nā'ib) was taken from everyday speech and then given one precise technical sense.
In everyday Arabic it means a deputy — someone standing in for another.
نَائِبُ الرَّئِيسِ (nā'ibu al-ra'īsi) — “the vice-president”
In Arabic grammar it means the word standing in for a doer that has not been named.