Oooooo! Grimm Reaper Ruby/RG AU sounds fun! Thigh how does it still take place in the current setting of RWBY if everything is still the same?
(Sorry for the delay! I was sitting on this a little bit because I was hoping someone would guess who the soul Ruby's holding in the OG pic is, since the answer to your question kind of spoils it, but alas, I will now proceed to nerd out over this incredibly self-indulgent AU idea--)
Grim Reaper!Ruby AU verse takes place mostly in a vacuum space between life and death, called the Inbetween. This version of Ruby exists there to shepherd recently departed souls to wherever they're supposed to go after death, where that is/what it looks like she is unable to disclose. Essentially she was created by the Brother Gods to facilitate the natural order of life and death that they put into place. While she is in this place she doesn't really intersect with Remnant and its people while they are living. Time passes, but she is not apart of that world. The only glimpses she gets of it is when she's bringing souls to where they're meant to go.
It's a lonely existence, and she becomes even more isolated after the brother gods leave. She spends several thousands of years alone, until she finally gets a friend: the one person constantly coming in and out of life and death.
Yup. Ozma (that's the soul I drew her with, btw).
See, since her job is to guide souls to where they're supposed to go after death, that includes bringing the souls of recently deceased reincarnating wizards back to life. (side note, she isn't the one picking the incarnations. That is entirely decided by the God of Light's magic, she's just there to facilitate the interaction.)
So it's mostly a story about the conversations Ruby has with the various Oz-carnations while he's in limbo, and extends over pretty much all of pre-canon.
It is a rocky start at first. An isolated, not-human Ruby is not very good at expressing herself or explaining what is going on. And Ozma, well, he definitely was not having a good time those first few incarnations. It starts with a lot of frustration and fear (especially for Ozma on that one) between them.
Ozma thinks she death itself the first time he sees her and is terrified. Later he comes to associate seeing her with the dread of knowing he's reincarnating again and all of the discomfort that comes with that. Maybe a little resentment too, because he assumes she should be able to stop his reincarnating (she cannot.)
Ruby on the other hand is a little startled, a little uncomfortable because she's never actually interacted with the souls. Once the shock value wears off she gets a tad depressed because she finally gets to talk to a real person, but they're afraid of/hate her. Later she becomes irate with him as early Ozma did a lot of stupid reckless stuff 'because he didn't really die' and she found his actions to be a horrific disregard of life (while he's getting yelled at for this is when he realizes it isn't just him, but also the souls of the people he bonds with and oh boy here's a mental crisis).
Angst aside, eventually the two learn how to talk to each other, and end up becoming each others biggest source of emotional support. For Ozma that means he becomes less afraid of dying and dreads reincarnating less, because he knows that Ruby will keep him safe through the process that leaves him very vulnerable. Ruby is also a major encouraging force for him, when the pressure of the mission gets to be too much. For Ruby, Ozma becomes the lense through which she gets to learn more about the world of the living, something she's always craved but was never allowed due to the nature of her existence. She gets to allow her curiosity to run wild, and it does wonders for her in developing an identity that's unique to herself and not just as servant to the Brother Gods. The brief intersections of time they get to spend together are very meaningful for the both of them.
(You mentioned RG in your ask. I'm a little hesitant to put a defined ship to this AU since the relationship is a little blurry. I kind of want to put this down as queerplatonic Ruby/Ozma. It's a bittersweet relationship, because they can only meet when Ozma dies, but both of them are firm on the fact that Oz should not ever try to die. I don't think it's meant to be a romantic relationship with this one, rather a general, intense emotional closeness. And of course, by the undefined nature of Ozmosis, it might include Oscar as well. Ozpin too, by that measure.)
To (finally) answer your question, back in real-Remnant the canon version of Ruby is never born. She does eventually end up in canon though! After Ozpin's death at the fall of Beacon, she reaches peak dissatisfaction with both of their situations and decides to do something she's never done before: disobey the gods. She crosses over into Remnant, something she was ordered never to do, and she goes to find Ozma's newest incarnation.
I'm still a little uncertain what happens next. Most of my brainstorming was pre-canon stuff XD. Anyway, the official name of this AU is 'The Reaper and the Wizard,' and the idea for it came from this writing prompt, despite the fact that nothing I've said here could possibly explain why.
(Thank you for the ask!! this is the first time i've written any of this down, lol. not sure how much sense it makes? eh. If anyone's curious and wants to ask more I will definitely answer.)