Uage of `ce que` vs `ce qui`

Question

As I understand it,

1. ce qui is used when referring to a subject, and ce que when referring to an object in a relative clause[1].

In my exercise book I found the following sentence

À cause de diverses formalités liées au décès de son père a Bruxelles, elle était obligée de séjourner encore quelque jours dans la capitale belge - ce qui arrangeait deux policiers.

which confuses me, as I would have expected the usage of ce que instead of ce qui. As I understand it, ce qui refers to the object of the relative clause (i.e. what the two policemen arranged) and hence should be replaced by ce que. What is my misconception here? Is my translation wrong or is there an exception to the rule (1.)?

Answer 1

Note the difference:

À cause de diverses formalités liées au décès de son père a Bruxelles, elle était obligée de séjourner encore quelque jours dans la capitale belge - ce qui arrangeait deux policiers.

Because of various formalities related to the death of her father in Brussels, she was obliged to stay for a few more days in the Belgian capital - which was convenient for two policemen.

vs

À cause de diverses formalités liées au décès de son père a Bruxelles, elle était obligée de séjourner encore quelque jours dans la capitale belge - ce que deux policiers arrangeaient.

Due to various formalities linked to the death of her father in Brussels, she was forced to stay for a few days in the Belgian capital - which two police officers arranged.

In the former:

Qu'est-ce qui arrangeait les deux policiers ?

In the latter:

Qu'est-ce que les deux policiers arrangeaient ?

Update: There is a nice comment below that I wish to add to my answer. It provides better insight to your query. (Many thanks to the teacher of French @Luke Sawczak for his comment and the verification as well!).

Your mistake is actually one of vocabulary, not grammar. There is a verb arranger that means to suit someone or to please someone. Thus the officers didn't arrange her stay, in which case they'd be the subject of arrangeait and you'd be right — rather, her stay suited the officers. You can find a clue as to the true subject in the conjugation of arrangeait, which is singular. Your original reading would actually require two errors, not one.