I used the term, 'either died or lost the gunfight'. Here are some examples:
1) Massad Ayoob collects many of these cases. Rich Davis, the man who invented second chance vests, took a bullet to the guts after emptying his 6 shot wheelgun at three armed thugs, hitting three of them multiple times.
2) Here's the case of Jason Hendrix (off duty, in a shopping center). He had a 5 shot S&W model 36, the suspect had a Glock 17. Hendrix shot the suspect 4 times out of five, twice hitting him in the chest, and then his gun went dry. The suspect shot Hendrix in the face, guts, arm, pelvis, and tried to execute him as he laid on the ground.
Shots Fired: Palm Desert, California 03•30•1996 - Article - POLICE Magazine
3) The death of NJSP trooper Lamonaco prompted the dept. to switch from 6 shot 357 magnums to the 9 shot HK P7M8. Lamonaco was shot by environmental terrorists who wielded browning hi-powers against the trooper's 6 shot revolver.
4) The ISP switched to the S&W model 39 (8 shot 9mm). In that time period, there were at least one, if not a few, cases where troopers would have certainly died if all they had were the 6 shot wheelguns. There was one case where the suspect counted 6 shots from the trooper's pistol, and after the sixth, charged the trooper with his shotgun. The trooper shot the suspect with his last few rounds. The suspect told his attorney he swore the cop's gun was empty.
5) There's the case in California, where at least one trooper was killed after his K-frame magnum ran dry. When he took the knee to reload, the suspect executed him with a 9mm before the trooper could close the cylinder.
That's just five that I remember off hand. there are many more cases where 5-6 were not enough.