Which is why we need a ruling on it.
I know I'm not Christopher, and my posts aren't official or anything, but I just talked to him and he says EoD keeps going, possibly resulting in multiple plays from Lady Luck. I don't know if he plans to come and give it his official blessing or not, but for those of you that just want to know, that's the ruling.
So End of Days will not destroy itself until there are no cards in play other than itself, Character cards and Relics. Glad to have that cleared up.
Correct! End of Days devours all!
* Looks around shiftily *
Except Relics.
And possibly things that Unity likes if she has a Bee Bot.
And actual Heroes and Villains, sidekicks are OK to be devoured.
Sweet, official ruling!
Also I'd like to be the first to jump on the vague connection to Raptor Bot in the above sentence.
It is clear that in this timeline the Final Wasteland is brought about by rampaging Mechanical Raptors.
You ain't kidding. I had my phone on the table when someone played EoD, now I canlt find it. In retrospect, I should have wrote "Relic" on it.
I use a rotary phone, it has intrinsic Relic status.
Except Indestructible cards? Right? 
I don't wanna get devoured…
I would assume this to be the case. Indestructible cards would be the exception to the general rule.
And Indestructible cards, which technically make End of Days incapable of ever finishing under its printed wording (it would continually try to destroy them and would tie the game up in an infinite loop, since it's not explicitly allowed to ignore them).
Alas, that is not how "rules" work. Exceptions only exist if they're specified; common-sense assumptions like "obviously it ignores indestructible" are directly contrary to the entire purpose of any variety of "rules" existing, since otherwise you could figure everything out for yourself with no need of the rules. Granted, Sentinels sort of vaguely encourages the use of a "Rule Zero" which trumps all other rules, but in an RPG context, "Rule Zero" only works because the Game Master is allowed the final word on any and all arbitrations. In a non-RP game, nobody has that authority, except Christopher in this case - so he has to explicitly say it ignores indestructible cards, or otherwise that's only a common-sense assumption, which is directly contradictory to the "letter of the law".
If you want end of days to work like a computer program, or a logic thread then treat End of Days as a cycle, it attempts to destroy every card, one at a time, then if there are any possible targets left, it tries again, and again, until it fails to destroy any cards at all. Then it stops.
Except that computer programs written to try to complete logically impossible instructions don't stop; they keep going on forever until the machine running them malfunctions or the cycle is otherwise broken. There's no real question as to how we should "treat" End of Days in practice; I'm just pointing out that in theory, it has no capacity whatsoever to ignore an indestructible card, or to proceed to its self-destruction and the rest of the game as long as an indestructible card exists. Since many other cards say "non-indestructible" where necessary, I think this one ought to as well. (That "indestructible" isn't quite the right word anyway, since the cards also can't be returned to hand or otherwise moved out of play in non-destruction ways, is a separate issue.)
Yes I'm being extremely pedantic, but then, if I were a computer programmer (and I'd like very much to be one, given the necessary knowledge and opportunities), that would be my job. Technicalities matter, particularly in the vein of anything that attempts to follow "rules" or "laws" of any variety; if you want to approximate, such things are worse than useless, as they become active impediments to the free exercise of creative judgment.
With the ruling you still get to decide if this edge case occurs whether you'd like to run down Kismet's villain deck or not. Or more accurately, try to minimize or maximize the chance of running it down but choosing whether to attempt to destroy "Lady Luck" itself first, or last. Though it might not be to the heroes' advantage to get hit by all the effects of her one-shot Luck cards while doing so.
It can be in the other order if something causes Fixed Point to be played out of turn.