https://en.wikipedia.org/wiki/Crush_syndrome
It's hard to understand why Snopes has this marked as a myth. The specific anecdote structure with the wife showing up is clearly a meme but that doesn't make it a mythical type of event.
We're much better at dealing with this situation in developed countries now. It's still a serious hazard. Around the turn of the 20th century it was very difficult to handle.
That doesn't seem to describe a situation like the ggp was talking about.
The key elements of the Snopes article are these:
-Victim was crushed by machinery.
-Victim is still alive.
-Victim is not in much pain.
-If the machinery is removed the victim will probably die quickly.
-There's time to have them communicate with loved ones, a priest, whoever.
There are literally videos of this situation on liveleak. It happens with trains, with elevators, with forklifts and freight, and most commonly with car accidents.
The reason you don't remove the person at first is that they'll bleed out. The crushing material is an effective tourniquet so the person just sits there, alive and moving.
By the time that emergency responders get there to address the blood loss crush syndrome is a definite possibility. The person is generally going to faint the moment the equipment is removed because of the sudden loss of blood pressure. If they don't die of blood loss then they may have kidney failure and die on the way to treatment.
Everything about this is shockingly common except bringing the victim's family down to say goodbye or bringing in a priest.
To suggest that this has not happened in any of the hundreds or thousands of crushing cases since the industrial revolution occurred is ludicrous. It used to be that companies provided housing for workers near the factory/trainyard/loading dock. It would often have been the case that the victim's family could get there before an emergency responder.
The sense in which this is a "legend" is that people claim it happened to a friend-of-a-friend or whatever, and it's true that's an urban legend channel, but the actual events are documented except for the dramatic last kiss. I wouldn't even be sure that isn't documented. I just haven't seen it.