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.