From what I can tell, the phrase "being warned" is not the same as a stand-alone gerund, such as cooking, studying, or running. For example, I could write, "Someone criticized my cooking" and stop right there, but it would be strange to write, "Can my car be repossessed without my being?" So I think we're dealing with a constructed participle and not a true gerund, so that "being warned" is the complete verb. To go back to the cooking, if I added our current phrase and changed the sentence, it would be something like "I don't like my cooking being criticized." It just seems like any verbal construction with "being" in front of another verb (being called, being harassed, being spoken to, etc.) is going to call for a different approach. To that end, I could write, "Can the group leave without me being called?" or "Can I take a trip to the island without my being vaccinated?" The difference is in the emphasis on the personal pronoun as an object (they should call me) or the information as a whole after the preposition (I can't leave without my vaccination).