my being vs me being
I have never understood why people say stuff like “Can my car be repossessed _without my being warned_?”. In my ears it should be “without me being warned”. Heck I would even prefer “without I being warned”. The only explanation I can come up, given that “my” is possessive, is that “being” is a noun which refers to you as a mortal being. But that doesn’t make much sense in the sentence since “being” is used as the verb. For it to work it would have to be “without my being getting warned”, or “without my being being warned”.
Am I right that this is just badly evolved english (although seemingly legitimate today) or am I missing something here ?