Here is what I think:
Standing is an intransitive verb, right? Yes.
Are the phrases "The ladder on which" and "began to slip " considered as an A. A. of place? What is A.A.?
if we changes change the position of the these this phrases clauses, we would have: "I was standing on a ladder which began to slip", where the underlined constituent would be not obligatory, right? I didn't get your point but I can tell you that there is a change in the meaning.
The ladder on which (on it, on the ladder) I was standing began to slip. In this sentence, the ladder is modified with which and it tells us your position with it. Which belongs to the ladder and you are on it. Emphasis is on your position here. However, this sentence doesn't sound me correct and I have doubts about using began with slip.
I was standing on a ladder which began to slip" .In this sentence which modifies the ladder , again, but the emphasis is not your position here, it is on the slipping ladder.