It is possible that the remaining last two tributes might get killed at the same time, for example, by a land mine explosion, and in that case the games will end with no victor standing.
Is there a reference in the original books as to what happens if nobody emerges victor in the Hunger Games?
There's nothing in the three books that explicitly states what would happen in the event that there was no victor. However, I think we can make some educated guesses about what might happen.
First off, it's extremely unlikely that the final two Tributes are going to die. The Capitol is going to make sure of that. The arenas seem to be completely under the control of the Gamesmakers, under the guidance of the Head Gamesmaker, so they aren't going to die from "natural" disasters, or even from things like mine explosions, as they'd no doubt disable those the moment it came down to the final two - unless they were necessary to force the two of them together.
Of course, it's not an entirely impossible situation. Katniss and Peeta could have very well gone through with the threat of eating the berries, and the Capitol would have been without their victor. And they need their victor. It's part of how they maintain their power. The Victory Tour - strategically placed halfway between each Games - is intended to remind the Districts that they're powerless. They take the victor, the strongest of the previous lot of Tributes, and drag them around Panem, putting them on display, and the Tribute has no say in the matter.
Let's assume that there was no surviving Tribute. What would the Capitol do?
First off, try to revive the victor. They have access to advanced medical techniques and equipment; depending on the severity of the injuries and exact cause of death it may be possible for them to revive them. They're not going to give up until they absolutely have to.
If that doesn't work, depending on the exact cause of death, they may very well lie. The 75th Hunger Games, the third Quarter Quell, demonstrated the Capitol's ability to manufacture recordings using an individuals voice. There's also the option of surgery to make somebody look like the winning tribute. If the tribute died from injuries, or blood loss, or exposure to the elements, dehydration or starvation, this may well be a viable option.
If they were, for example, blown to pieces then this would be impossible to sell; you can't fool an entire country who saw the explosion happen on television into believing that you managed to save them.
No, there's no such reference. I obviously can't give you a link or a quotation to prove a negative, but it's the kind of thing I would have picked up when reading the books, if it existed.
There is no canon explanation as far as I know. However, it would not be a good thing. In the first book, when Seneca Crane changed the rules back to only allow for one victor, Katniss and Peeta had decided they would commit a double-suicide, so that the Capitol would not win again.
Crane stopped them before they could complete their plan, and crowned them both as victors, but all that can be said about having no victor is pure speculation. Ultimately, each year the Capitol is the victor, because the games keep each district from rebelling the way District 13 had. When Katniss volunteered was the first year that the Capitol lost the Hunger Games, and you could count that as there being no victor, because even though Katniss and Peeta won the games, the had still had to kill all those other tributes, and no one can consider that a victory for someone so young.
I actually think this would be quite unlikely. For 2 main reasons.
So that's why I think it's unlikely, but it could happen still.
Really it could be possible under very rare, very special circumstances. For example, say in the final battle of two survivors as references to how Haymitch won near the arena edge, one tribute throws an axe, the other ducks and stabs the other one in the eye to the brain, killing them as the axe hits the force field and bounces back, before slamming into the back of the head of the supposed victor, killing. Bam! No victor. Or like Beetree blowing up the six victors, if they had calculated the explosion extremely wrong and the explosion shot off shrapnel of bone, which was lodged into the heart or head... Anything that doesn't kill the victor, meaning head blown to pieces or heart shot, one of them will be resuscitated somehow, or retake as has been said...
Nothing, they will do nothing about it.
