First crack theory after chapter 97.
I was staring at Rin's panel where he's "spreading" all the flames. Aside the prominent large flame coming out of his chest (hinting that his demonic heart is about to come out of it?) his skin is indeed starting to necrotize (as someone pointed out too). Well, I was thinking. This is like what happened to Izumo during her arc. So I picked chapter 60-61 and read 'em again.
Izumo was necrotizing 'cause she couldn't handle Nine Tails, an high-level demon (as explained by Yukio). So, what I get is that necrotizing is like a body's "reaction" to a possession it can't handle. I guess this is somehow what's happening to Rin right now. He can't handle that much flame power (or whatever it is) and his body it's necrotizing as a result.
Or there could be another esplanation. Also in chapter 60, Gedouin tells Izumo "Don't resist. Give yourself to Nine tails." I think it could mean Rin's necrotizing 'cause he's struggling to "resist" to the flame power and if he will "surrender" to it, he'll stop necrotizing. But he will be completely "possessed" by it (the flame power). And, also in chapter 60, Gedouin mentions that "This device (the mask) will force the possession to take hold. But this procedure is for a -chosen one- fortified by the -elixir-."
Okay, I got some weird ideas out of this. What if the Illuminati are planning to use the elixir on Rin to force him to get possessed by Satan? (now that we know Satan wants to use him as a vessel). I can think that the reason Mephisto trained Rin to handle and control the flame was all part of a plan to "boost" his compatibility and tolerance of Satan's possession. Just like Izumo needed a certain "percentage of compatibility" with Nine Tails to get it to successfully possess her.
Also, what if this is all those chosen ones and/or high-level demons are needed for? To create an elixir strong enough to boost Rin's compatibilty with Satan's possession. In chapter 80, Lucifer stated "It may become necessary to prepare Father's body with the materials we already have." If Satan's willing to possess Rin, why the need to make him another body? Maybe in case even Rin will not be able to handle him?
But if I read Lucifer line in another way: "It may become necessary to modify/alter Rin's body with the materials we already have (by creating an elixir though them)".
Aaaaalso, on another note, if this is gonna go the way I think, I can already picture the anime's counterpart where Rin's tied to a cross thing spitting blood to open the Gate and... yup, Yukio offering to take his place. What I see in the manga is: Rin will be injected the elixir but it won't go that smoothly. So Yukio (also willing to grasp this chance for his own power-seeking puposes) may offer himself on his stead. But the one reason I can't actually see this is that'd be a repeat of Izumo's mother offering herself on her daughter stead and so on.
Anyway. Honestly, I can't remember if it was ever mentioned how the Illuminati make that elixir in the first place. I should read those chapters again, I guess.
Edit: on second thought, I was thinking, what if the Illuminati could choose to use Yukio as a vessel for Satan in case Rin won't be able to sustain the possession since if the elixir, when injected, can potentially kill the subject, while Yukio is "protected" by Satan?
And, to add to this: Lucifer said it was important that Yukio chose to join them on his own free will. Maybe he meant it was important since if Yukio is willing to cooperate that'd make it easier for him to accept/endure a possession unlike Rin who'd (I guess) refuse to accept it (willingly).