It seems to me like, even aside from the submitted roster issue, football would be the least likely sport for this to happen in. Football teams are very large, and you only actually need 11 of them, and unlimited substitutions are allowed. Even if they somehow had so many injuries that they were literally down to only 11 able-bodied players, I’d think that a pro, even one tired out from the last play and playing the wrong position, would still do a better job than some rando from the stands who played in high school.
The Cowboys have only lost twice to the Niners twice in the playoffs; both of them epic NFC title games. One was the “The Catch” game where San Fran beat Dallas 28-27; the other was the 1994 NFC title game where San Fran beat Dallas 38-28. It would have been unconscionable in both games for the Cowboys to have left the field early.
I recall the Simpsons doing a gag based on this once - Homer has bet on the Raiders based on a scam mailer he got, and when the actual game happens they have so many players injured that they conscript a gang of hobos from a local bar. 
It certainly wasn’t “The Catch” game, because I was there, and the one I saw was on TV. It’s entirely possible that I’m wrong about it being a playoff game; maybe it was a game they needed to win to get into the playoffs.
Vince Papale actually played pro ball with the WFL Philadelphia Bell so he was hardly a “fan out of the stands” as the movie portrays.
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Cowboys versus Redskins, January 22, 1983. Washington won 31-17, not a blowout. Washington was leading and running out the last few seconds in Dallas territory, and they ran their fourth down play, and then, no matter how long they’ve been playing, players forget that the clock stops on a change of possession, and players from both teams started jogging off the field. They weren’t quitting, they just thought the game was over. But the clock had stopped with a few seconds left.
Eventually the refs dragged enough people back to run a play, and Drew Pearson came out and ran a kneeldown. Not very exciting stuff, actually.
Ah, thank you, that pretty much corresponds with what I dimly remembered. It was a playoff game, the game was out of reach for Dallas but not a blowout, and the game circumstances resulted in the need for the Dallas offense to run a play from scrimmage with just a few seconds left, without having been on the field for the previous play. And Drew Pearson took the final snap. I guessed wrong about the field goal and the opponent, but I’m going to give myself a B+ for getting that much right, especially remembering Pearson by name, when it’s been over 35 years since I’ve thought about it.
But with my renewed confidence in my memory, I’ll push back a bit on your implication that it was just an innocent brain fart, or at least, no more than that. Yes, anybody can momentarily forget a rule, but if they do, they have coaches and refs there to remind them. My memory was that after some confusion, the (Skins) defense was on the field waiting for the Dallas offense to come out, but the announcers weren’t sure whether they would since they couldn’t possibly win, and that this situation lasted at least a minute or two. Eventually, as you say, they “dragged enough people back to run a play.”
Not quite the same thing as the OP, but back in 1912 the Detroit went on strike (in support of Ty Cobb, who was suspended for beating up a heckler). Rather than forfeit the game, the management rounded up a bunch of amateur players and lost 24-2.
Which, when you think about it is pretty impressive. On the pitching and defense side of the ball, obviously a ridiculously poor performance, but scoring two runs is pretty respectable.
(My emphasis.) That is what is known as burying the lead. I’m getting a lot of pictures in my mind, and all of them are funny.
Any day that the Skins beat the Cowboys is a good day.
That sounds about right. I don’t doubt that grumpiness played a part.
Rather like the often-seen situation where teams have to be “dragged back onto the field” for meaningless PAT attempts after time expired, which requirement I see has been mercifully eliminated for the 2018 season.
It’s been a while since I saw Invincible, but I believe the movie did make it clear that Papale had had some experience playing ball at a fairly high level. That was the impression that I had, that he’d taken a shot at pro ball,and just didn’t make it. Of course, “random Eagles fan tries out for, makes the team” is a better story, so I may be misremembering.
I saw the movie about ten years ago on TV while I was doing something else, so don’t quote me on this, but I thought it just showed him playing football with friends from the bar, where he was clearly the best player among them.
Googling just now for his actual record, I see he got a private workout from the Eagles based on his WFL performance. That DEFINITELY was not in the movie. In the movie, he was at some kind of publicity stunt open tryout with a bunch of mokes, and impressed the coaches enough with his 40-yard dash that he was given a chance to make the team.