Yes, I did have this happen due to seatbelt and airbag in a high speed wreck.
Because I was already on PPIs I had had non-acid reflux for at least 25 years and no bad acid erosions, I would not have had surgery but for the accident. I already had a small hiatal hernia, but those are of no significance normally and just about
everyone gets them at some time. I have a weak swallow due to having polio as a child, so I can't swallow large pills and have had trouble with chunks of meat that were not chewed well enough.
However, a paraesophageal hernia, where the stomach stays in the chest, is dangerous. If the stomach rotates it can start dying immediately and you have to be rushed into surgery with only a 50% chance of survival. Since it will not correct itself, a paraesophageal hiatal hernia is a clear indication that surgery is necessary.
This surgery is done exactly like the Nissen fundoplication, laparoscopically. Since the stomach has to be pulled down from the chest carefully, it takes a good bit longer (mine took 4 1/2 hours), but is probably no more dangerous in the hands of a top, experienced surgeon. I was not the best candidate for any surgery because of a previous heart attack and my age, but my surgeons are tops in their field here in Pittsburgh, and I had a good outcome.
I wouldn't recommend going to a surgeon who hasn't done thousands of these procedures for a paraesophageal hernia. Less esperience is probably fine for routine surgeries, but this one takes a bit of doing to get it right. Since I don't have a strong swallow, the procedure selected for me was called a Toupet fundoplication. It's a partial wrap done in the same manner as the Nissen.
Let the surgeon choose the procedure based on your tests, but there's no question that surgery is necessary for a stomach stuck in the chest.