This has already happened. Models developed in the 1990s didn't match what happened in the 21st century. The resulting controversy is called the pause. Why did temperatures stop rising when models said they should continue? We didn't stop putting CO2 in the atmosphere after all.
For better or worse, the controversy was resolved by scientists "correcting" the historical temperature datasets to erase the pause from the record. The data was brought into line with the theory. You can go read old news stories or articles about the pause and look at the temperature graphs in them, then compare to the current, up to date temperature graphs and see that they don't match.
If you like there's a talk here by a guy who started out as a skeptic because he kept spotting errors in studies, and became a peer-reviewed, published climate scientist. He's still a skeptic about the models used to predict the future (he says he thinks the basics of climatology are sound though):
https://www.nicholaslewis.org/wp-content/uploads/2019/09/Lew...
That talk is quite technical but might provide some answers to how the models could be wrong. Ultimately nothing surprising: they're based on major approximations and the underlying datasets may have issues. Go read his papers for more details.
I think it's a really interesting question, even though on a charged topic and difficult to forecast.
Balance of feedback systems? There are so many feedback systems here, positive and negative all overlapping. Even if you are 95% sure you have each one figured out, after a little over a dozen factors that error compounds and you're at around 50/50 of getting something wrong.
Of course, could be wrong in the other direction too... that's why errors are bars not arrows.
Note: Feedback systems here are not under-studied, they're just hard to model. This isn't an example of a black swan that would devastate the discipline, if that's what you were looking for. Those might be... supervolcano? Nuclear war? Atmospheric scrubbing technology breakthrough? Even those have calculable effects. If there's some radical unpredicted shift I can't imagine it being along the lines of "water vapor and CO2 don't actually warm things," that's just too well confirmed.
Most likely, if climate research is found to be far off the alarming predictions made by most institutions, we'll chalk it up to political meddling/statistical fubbing and move on. If the lifestyle changes for most of the polulation are already in place by then, many will believe it was "for the best, anyway", and I'm inclined to agree with this view - our response to climate change is more important than if climate change was primarily our fault to begin with. I'm not advocating for skewing research in favor of one position or the other, but it enables a public forum of such scale that at the very least, prepares us for dealing with ever-increasing scopes of global issues that impact all life on Earth, which will come in handy when we progress to the point we're dealing with the ethics of extremely advanced technology.
Presuming we don't lose key information (e.g. deliberate erasure of the NOAA archives), we'd treat it in the same way as the current investigation; find what changes are required to the model to make it consistent with the data.
> we'd treat it in the same way as the current investigation; find what changes are required to the model to make it consistent with the data
If that is how it is currently done, I have a big issue with it. It seems like the model is not being treated as a forecasting model but rather as a purely academic one ('if we make these assumptions and have these initial conditions, how does the behavior of the system evolve'?), while being sold to the media, politicians and the general public as a forecasting model that is assumed to have very strong predictive power.
If in 50 years, we find out that the predictions made by our models had been wrong (either the measures we take to reduce CO2 don't lead to the results we expected, or the warming we see is outside of the expected ranges) - in the post-mortem of the models, what would we likely say had gone wrong?