I don't think it's almost impossible - at least twice in the history of the game 2 rats have failed to finish the race, including this season. I think it's actually quite likely they are going to have to deal with this situation sooner or later.
Whether there is an established plan is another question. Your solution could work, but I would probably say that no rat "finished" in third so regardless where it ended up on the track they win the third prize by default. Some rats could have been faster and others might have stopped later, so it would be a mess I'd rather avoid.
To take it to an extreme level, if all the rats failed to cross the finish line I would give away the car. We'd also be looking to solve this issue pretty quickly.
At first my thought would be "If three rats don't finish, just stop tape, get five new rats and reshoot." After all, that's almost certainly what they've been doing with stopped Plinko chips, and I imagine it'd be kosher with S&P as long as they did something like putting it in the game's official rules to make it clear that they weren't doing it to favor any particular contestant.
But after thinking about it a little more that wouldn't work. What if the two rats that
did finish happen to be the two the contestant picked? Wouldn't it suck for the contestant to have seemingly won a car and a large prize only to be told because they missed out on a chance to win something cheap like an Xbox One they have to scrap the results and try again? Would S&P be fine with it?
It doesn't seem like something they'd do. If a contestant had to give up the car they "won" just to try again for another chance at something insignificant, they'd be rightfully very angry, whether it's "legal" or not...so "award the prize by default" would be the next best option IMO.