Why is it rare to see unusual "special" opening preparation by trailing player late in a match? Taking the recent Anand-Carlsen match as an example, I know that grandmasters spend incredible amounts of time in opening preparation, and Anand's play to refute certain lines of the Berlin defense was impressive.

But once reaching game 10, 11, or 12 and desperately needing a win, why don't players make an effort to force the game off into some opening line that the opponent almost certainly hasn't prepared for? Not into some fringe or unorthodox opening, but into solid openings that are just much less familiar for the opponent.

Much the same way that an American football team must spend at least some small amount of time practicing "trick" plays, like on-side kicks or throw-back passes, or much like a football (soccer) team might practice very special free kick formation for late in a game when a goal is needed very quickly -- shouldn't it be normal to prepare for a championship match by spending at least a small amount of time studying some very different openings that the opponent has not faced recently or does not appear to be as strong in?

I'm not endorsing these as candidates for specifically Anand v. Carlsen, but I might have expected to see some different variations of Sicilian, or to see Dutch Defense, Benoni Defense, or to see Reti opening, and to play in lines that don't transpose easily to positions that are similar to the main lines played (Grünfeld, Berlin, etc.).

I'm not saying Anand's openings were the problem in the match -- he often played well with great opening prep and blundered later on. 

I am just asking why it is so uncommon to see players deviate to some "special preparation" in late stages of a match when they are trailing and need a win. 

Wouldn't that be one of the scenarios that they prepare for specifically prior to the match starting? "What if I find myself down 1 point late in the match and my opponent has shown clear strength in the most frequent openings from the match? How will I steer the game into unknown territory?"
It happens, but there's a reason why it doesn't happen often, and, when it does, why it doesn't work.

First off, there's a psychological reason not to do it; it's uncomfortable. If the match is going badly for you, it's natural for you to fall back on familiar weapons: positions that you know how to play better than any others. When you do that, when you stand on familiar ("home," if you will) ground, you feel more secure and play better than if you're in less familiar territory. And when you play better, you're more likely to score better.

Also, there's the unknown. When you're down by a point late in the match, a single failure ends your chances. And, when you decide to divulge radically from your "normal" game approaches for this one game, you don't know with certainty how well your opponent can play those positions. So you divert time away from preparing to play comfortable positions even better than you currently play them (after all, no one plays their comfortable positions perfectly, there's always room for improvement) to learning how to play a completely different position passably well. And, when the day of the game dawns and you uncork it, you find out your opponent actually likes to play those positions, just never gets the chance to because opponents haven't so far let that happen. And down go your chances of leveling the match in a flaming crash.

Romantic notions like risking everything on one wild roll of the dice don't occur naturally to the vast majority of top chess players, because the tendency to do so keeps them from making it to the top, except in the rarest of circumstances.

A GM once told me chess was a little like tennis; "sometimes the only thing you can do is hit the ball back over the net and try to give your opponent another chance to make a mistake."

You're far more likely to see a player pull divergences like that that early in a match than late, such as Fischer pulling out 1.c4 to open Game 6 of the 1972 match (that match was for 24 games, so G6 there would have been like G3 of Carlsen-Anand). If it doesn't work, then the player still has the energy to save the draw if possible, and time to recover from the failure if not.