Out of my field, but I'll take a bit of a stab seeing as martial arts and combat sports are my hobby.

The saga of Frank Dux might be the best place to look.

His wikipedia page is a bit underwhelming; google can provide many more articles, but here's the tl;dr version.

Frank Dux is infamous in the martial arts community; he claims to have entered and won such a secret "kumite" tournament in the 70s. But he claims a lot of things, and is pretty widely regarded as a liar.

Why do I bring him up? Because not only has anyone been able to come up with any claims that he participated in such a tournament, nobody has ever been able to provide any meaningful evidence that such a tournament has ever taken place anywhere.

So lack of evidence aside, let's consider the concept in the abstract for a bit here.

Prize fighting (like all professional sports) has always been dependent on an audience and promotion. The audience pays the fighters for the entertainment of getting to watch the fight, and the promoters create the audience by convincing people that the fight will be significant and entertaining.

Presumably, such a "deadly kumite" would only consist of the best fighters in the world, fighters who had built a reasonable reputation (enough of a reputation to get an invite). And they get that reputation by fighting a lot, and by winning fights. But at the same time they get the public's interest and a following. If a tournament like this was to occur, you'd pretty much see a number of famous fighters all disappear at the same time, and that would draw interest. Even if it was just a bunch of prospects (i.e. not the best of the best), the promoters and scouts and coaches who keep an eye on such things would probably notice something funny having happened int hat respect.

The risk vs reward for the plausibility of fighters accepting an offer to participate seems kind of sketchy, too. A top-level fighter who makes good money and is practiced within a given rule set isn't going to accept a sketchy offer to enter some secret lethal event.

Lastly, fight tournaments tend to be kinda underwhelming. The last high profile MMA tournament, the Strikeforce Heavyweight Grand Prix, took close to a year to complete through three rounds of competition, due to injury and recovery, and was still won by an alternate. The Bellator and Ultimate Fighter tournaments use a ruleset designed to decrease the chance of injury layoff, and still take months to complete. Lots of the famous one-night tournaments, the early UFC tournaments, the Pride GPs, or the K-1 Kickboxing World GPs, were and are disrupted by injury, forcing alternates to step in (see UFC 3), or feature rulesets that try to minimize the chance of a tournament bracket getting disrupted, and still have problems. A high level fighter and his or her coaches would be acutely aware of these dangers, and probably decline for those reasons, sketchiness aside.

Now this isn't to say that people haven't done things that might resemble "Kumite" - abuse of prisoners, "bumfights," illegal unregulated prize fighting gone wrong, etc - but usually this is under duress, not invitation to high level, highly-trained athletes.

tl;dr such a tournament wouldn't be feasible to find fighters for, to operate, or to keep secret.

This relates to the comment on Frank Dux that was deleted.

Portions of this comment violate the 20 year rule, but that's because the easiest evidence in this regard is recent stories, not stories from the more distant past.

Dux is a serial exxagerator if not an outright liar.

However, we certainly have many instances of there being organized illegal underground fights, some of which are more extreme than others. Although it breaks the 20 year rule, see a news story about illegal, underground UFC fights in melbourne

this discusses unsanctioned bare knuckled boxing in England including a reference, albiet unsourced, to a man being killed in a fight in the 1970's.

You also have things like Savate which is, as a community, quite open about its street fighting roots.

This gets into very local history, but in almost any community you care to dig into, you will find examples of people being willing to fight for money, and others who want to watch and to gamble on the results. Throughout history, is it likely that from time to time, people have died from injuries recieved? I would say it's almost a certainty.

On the other hand, you probably won't ever find some nefarious rich person on a secret island who hand selects combatants to fight to the death for his own personal amusement. These are urban events not unlike cockfighting or dogfighting. They're there to make money for promoters and gamblers.

No, probably not. There is proof, however semi-legendary, that many of the larger schools of martial arts in Japan and China would hold large violent tournaments but I've never seen any formal research to see if it's true or just an exaggeration of the more common ritualized tournaments that were held before the 20th Century.

There's also lots of underground fighting promotions across the world, especially common in unregulated prisons. The logistics of setting up an Enter the Dragon tournament is pretty close to impossible though as you'd need a worldwide martial arts community, a safe but unregulated spot, a prize that fighters would care about (A cash purse doesn't interest everyone), not to mention the ability to recruit or invite the right people.

If you take a look at the more unregulated fighting promotions ala Kimbo Slice, you'll notice that he mostly fights unskilled fighters or actual homeless people before he joined an legitimate promotion only to be humiliated.

The only real example I'm aware of is from the documentary Knuckle which follows a decades long bare-knuckle fighting tournament between three Irish traveling families due to some old feud. It's not martial arts but it's the closest thing to a repeated non-regulated non-cash fighting tournament I know of.

(Sorry to skirt the 1994 rule there but research on people getting beat up wasn't exactly robust before then.)

A somewhat related type of anything-goes fighting competitions are catch-as-catch-can wrestling matches in the American carnival circuits of the late 19th and early 20th centuries. These wrestlers, or hookers, travelled the country, learning and trading martial techniques from other hookers. They would then hold prize fights against the public, trying to throw the fights by hooking their opponents, forcing an instant submission.

Someone else mentioned the 100-man Kumite, and that along with other events in the life of Mas Oyama approximates an answer to this question.

The Gracie challenge is also similar, as is Vale tudo in general.

Are there any historical examples of invitation-based tournaments that were well publicised at the time?