Kung-Fu fighters pop up from time to time in MMA style fights. Early on in the UFC, there were a small number of kung-fu fighters. But by the end of its first year, you didn't see any. Why?
Well there's a reason for that. The first UFC's were open to all. They were very much about putting style vs. style. So they had karate, Taekwondo, kung-fu, wing-chun, judo, wrestling, etc. It was pretty cool.
But after a brief number of UFC's, a pattern emerged: Grapplers generally "owned" the strikers, who were mostly traditionalists and "purists" with no knowledge of grappling whatsoever. It was embarrassing for the traditionalists. Brazilian Jiujitsu emerged from obscurity to become the most well known and well respected styles that prepared people for MMA fights. Karate, kung-fu, and other traditional arts were starting to be seen as inferior.
Because of the influence the early UFC had, a lot of new students rushed to learn Brazilian Jiujitsu, Judo, Sambo, Wrestling, Submission Grappling, and Shoot-fighting. From this pool of talent came the next generation of UFC fighters. This new generation of fighters understood the value of grappling, and especially ground fighting.
At the same time, right after UFC 1, there were many local MMA venues opening up all over the U.S., Canada, and the U.K. It was in these local competitions where the new generation of fighters got their first fights. Every now and then, traditional stylists such as kung-fu fighters would enter these local MMA competitions, but they generally didn't win without grappling skill.
Then the UFC changed a bit. It became more selective. Instead of allowing anyone to enter the UFC, they would only look at fighters who had fought and won in local MMA competitions. They were looking for the best fighters, not the best stylists. Kung-fu stylists generally would not be able to win those fights enough to be recognized by and brought into the UFC to fight.
And now forward to today. There are local, regional, national, and international MMA competitions everywhere. There are now enough fighters to have organizations other than just the UFC. But the UFC is seen as the organization with the most elite competitions.
So your best bet for seeing how kung-fu stylists do in MMA is to actually look for stuff outside of the UFC or any other national or regional MMA organization. These would be local MMA competitions. Cage matches, tough man competitions, etc. Only there will you see newcomers with no fight history being allowed to fight, and so you sometimes can see kung-fu fighters.
Why, though, would kung-fu stylists not do well in MMA fights?
The answer is: You perform the way you are trained. It's not about the "style". It's not about the techniques. It's how you train that matters.
Kung-fu training rarely involves non-compliant, live partners who are trying their best to win against you, in matches that allow all 3 ranges of combat: free fighting, clinch, and ground.
If you don't train with people who are trying their best to take you down to the ground and submit you, you won't know how to handle that when the time comes to defend yourself from it. If you've never trained with partners who are allowed to grab you, throw you, kick you in the legs, punch you in the face, etc., then you'll be lost in a competition that allows those techniques.
It's even worse if you train in a style that doesn't even do competition at all. This happens in many kung-fu schools. In those styles, you're either just doing forms and punching to the air, or maybe you are lucky enough to have some partnered activities, but the partnered stuff is compliant and not "live".
By compliant, I mean that your partner is not resisting you. He's just letting you do stuff. He might throw a punch, for example, and then he stops and lets you do any number of crazy things to him. You might grab his wrist and yank at it until it locks his arm. And then you perform a standing arm bar. But he lets you do that. He doesn't try to pull his wrist away when he sees you reaching for it. He doesn't try to keep his elbow from being locked.
And by "live", I mean that your partner is thinking and able to change what he's doing on the fly, to make you aware of your problems. He's not just a robot, programmed to do one thing and stop. A "live" partner will not stop after he throws that first punch. He'll do another punch when he sees that you're too open on one side. He'll try to trip you when he sees that your stance is too wide. Etc. The most "live" a partner can be is during a sparring session, where things are done completely at random, and you have no idea what your partner will do next.
Another aspect to this training is speed and power. It's easy to practice trapping a punch and counter-striking to the face when things are slowed down. But speeding it up and adding power might show you that your elegant drill simply doesn't work at that point.
People who train in kung-fu styles have a lot of excuses and reasons why they don't train the way MMA trains. The most common reason they claim is that their techniques are "too deadly" for competition. They also disagree that ground fighting should be developed at all, because it would give students bad habits. They basically claim that being on the ground is dangerous in real life, for a variety of reasons (mobility, multiple-attacker scenarios, broken glass and used hypodermic needles, etc.). They would rather put all of their training into learning how to fight on their feet, instead. And they even dislike the notion of sport fighting, claiming that violates the principle of Wu De (martial ethics and code of conduct). For these and other reasons, they seldom even consider fighting in MMA competition.
By the way, there are good rebuttals to all of those claims. But we can save that discussion for another question.
Another thing to realize about kung-fu is that the styles are highly revered by their students and teachers, almost taking on religious significance. Criticizing any aspect of your kung-fu style is just not done. Kung-fu practitioners have faith that the traditional, old ways of training are the best, that their instructors are always right, and that their particular branch of kung-fu is the best. Each style passes down oral histories of their founders that make them sound near god-like. They talk about proponents of their style that once fought 30 people at a time and won, for example. And since their styles are generally thought to be "perfect", it means that if anyone does poorly using it in a fight, it's because that person just didn't train hard enough, wasn't very good at it, or may have had some sort of character flaw - laziness, egotistical, selfishness, etc.
So convincing kung-fu stylists that they need to train a different way or to start entering MMA competitions to test their skill is an uphill battle. It's just not very likely to happen on a large scale.
Incidentally, MMA is just starting to take root in China. It's unknown at this time how successful it will be at attracting students in a culture that's so deeply embedded in kung-fu.
We all would love to see a "pure" kung-fu stylist come into the MMA world and succeed. That would be amazing. There's no technique that you can see in MMA fights that isn't already in kung-fu. But like I said, it's not the technique that matters, it's the way you train. For that reason and the reasons discussed above, I doubt you're going to see any pure kung-fu fighters go very far in MMA.
Hope that helps.