2.3.1 is a single word — , when
not [already] expressed — and it governs the whole chapter that follows. A case
ending appears on a word only if the verb has not already expressed that role.
That one word does all the work that textbooks attribute to "the passive voice":
रामः रावणं हन्ति ।
Active. The verb हन्ति expresses the
agent (its ending is 3rd singular, agreeing with Rāma). So the agent's role
is expressed — no case is assigned for it, and राम appears in the bare
प्रथमा. The object is unexpressed, so it takes द्वितीया by
.
रामेण रावणो हतः ।
Same event. Now the participle हतः agrees
with Rāvaṇa — so the object is expressed, and takes no case for its
role. The agent is now unexpressed, and 2.3.18
gives it तृतीया.
This is why the agent and the instrument share a case.
कर्तृकरणयोस्तृतीया — one sūtra, both roles. Not a coincidence, not two rules that
happen to collide: Pāṇini states them together because in an unexpressed position
they behave identically. A textbook that teaches "instrumental = by/with" and then
treats the passive agent as a special idiom has hidden the rule.