General relativity (and other theories) when proven wrong

My question would be, what happens in the scientific community if one experiment proves it wrong

We have already seen what happens in this circumstance by looking at what happened to Newtonian gravity.

First, well before the development of general relativity there were observations that did not fit with Newtonian gravity. For example, Uranus’ orbit did not match Newtonian predictions. It was found that by modifying the predictions by including an unobserved source of gravity, the data could be coerced into fitting the observations. Subsequent observations confirmed the planet Neptune. As another example, Mercury’s orbit also did not fit, and a similar additional planet named Vulcan was proposed. The planet Vulcan was never observed through other means.

Now, afterward general relativity was developed. It explained the orbit of Mercury without requiring Vulcan. In addition, many other phenomena were predicted and discovered. Many of these phenomena were not predicted by Newtonian gravity or the wrong value was predicted. Through the course of these observations Newtonian gravity was explicitly falsified.

However, after Newtonian gravity was falsified it still continued to be taught in schools. The Apollo space program and other spacecraft successfully reached their destinations using the falsified Newtonian gravity theory.

The thing is that although the theory was falsified it had also been verified for centuries and none of that verification was removed by the falsification. Newtonian gravity continued to accurately predict all of the phenomena that it had ever been shown to accurately predict. If you were only interested in those previously verified phenomena then you could continue to use Newtonian gravity with confidence, and there is a strong incentive to do so because it is computationally far simpler than general relativity.

So, at some point when an experiment falsifies general relativity then new sources will be sought and if they cannot be found then that will place limits on its domain of validity, but it will not reverse any of the evidence that validates it within its domain of validity. Furthermore, just as general relativity needed to reduce to Newtonian gravity in the appropriate domain, so any future theory will need to reduce to general relativity in the appropriate domain.

If the future theory is computationally more difficult than general relativity, then we would continue to use general relativity just as we have continued to use Newtonian gravity. Thus, we would fully expect future students to learn general relativity just as current students still learn Newtonian gravity. General relativity will not go away, even after such an experiment

Words like "proven" and "wrong" have to be used carefully in this context. It is more meaningful to talk about "accuracy" and "limits". If an experiment was conducted tomorrow that contradicted general relativity it would by no means make general relativity a useless theory, nor would we get rid of it.

The purpose of theories in physics isn't to "prove" anything about the real world. This isn't even something they are capable of doing. Their purpose is to as accurately as possible predict the outcome of experiments.

Of course if there comes a time when a prediction of general relativity is not found in nature the likely reaction will be to attempt to reconcile the theory with the experiment, rather than throwing it out and starting from square 1.

Every currently accepted physical theory will likely be eventually found "wrong" at some scale. But all their predictions have already been experimentally verified a zillion-and-one times at the scales currently accessible to apparatus we know how to construct. So all these theories will forever be valid approximations to "the truth" at these scales, i.e., any more foundationally correct theory will necessarily reduce to our currently accepted approximate theories at these scales.

Take Newtonian mechanics, for example. Go too fast and it fails, requiring the use of special relativity. But $\sqrt{1-v^2/c^2}$ reduces to $1$ when $v\ll c$, so special relativity reduces to newtonian. Or study very small masses and it again fails, requiring quantum mechanics. Or study very large masses and it fails yet again, requiring general relativity.

And since you bring it up, maybe even general relativity will eventually fail. For example, maybe $G$ varies over cosmological times, which would require some kind of modification to general relativity. Oh, and maybe it might be this kind of modification -- https://pubs.giss.nasa.gov/abs/ca00010g.html But even if Canuto, et al, are right, general relativity will remain a valid approximation at the time scales accessible to our currently available apparatus.