Has it ever happed on Jeopardy! where no one had any money at the end of the Double Jeopardy round? None of the contestants would be able to play the Final round. What happens during the show - what do they do with those extra few minutes at the end?
Since they tape these shows well in advance of their air date, I suspect that such a show would simply not be broadcast.
I also find it highly unlikely that the situation has ever come up.
It’s happened in celebrity tournaments, but not in the real ones. There have been rare instances of 2 people in the red, but not 3.
The show is tightly scheduled well in advance. Each taping day covers an entire week’s worth of 5 shows, and they’re taped in real time, too. If the scenario happened, it would be shown.
Will wonders never cease?
I remember reading a long time ago on their web site that the first show they ever taped with Trebek ended with all players at zero dollars.
They all risked everything in Final Jeopardy and missed it. They all came back as one day champs with a one day total of zero.
The double zero thing has happened more recently as well. I was watching sometime last year or the year before and two people made it to Final Jeopardy and they both crapped out on the answer. Came back the next day, looking mighty sheepish. 
Tenebras
I would think that “Jeopardy!” would still show any show that ended up with no one going to Final Jeopardy because of the producer’s standards and practices. After the quiz show scandals of the late 1950s, the government has pretty tight regulations on game shows.
Also, the sponsors still want to give out their products.
It’s also possible that the official rules has a contingency for this.