AFAIK, there is no such rule. が alternates with を in some forms (potential, desiderative たい, etc.) and for some “double-が” verbs such as わかる (though the を form is considered improper by some), and that’s it. As for が->の that conversion should be always available in relative clauses (EDIT: when there’s no object in said relative clause) and never available anywhere else, so it’s fairly easy.
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