After a 3 year hiatus I return with an answer that I hope doesn't get torn to shreds by newer members here:
I'm going to start out with a more general answer: NOTHING done as a corrective measure (ADR, 'fixing in post', etc.) is necessary to do on a film set if it is properly planned for and solutions are brought to the table well enough and early enough in pre-production. It all depends on the directors, producers, and other team members of the production crew cooperating with each of the other departments and deciding what takes precedence for that given scene.
Does the violin performance play such an important role in the storytelling of the film to warrant ensuring the performance is captured perfectly? If it does, and each of the other departments agree, then solutions are worked out to capture it: be it with hidden mics, proper lighting that allows for a decca tree setup if it is more than one violin or simply agreeing not to give any verbal instruction during the take so you can record the sound properly, or you pre-record and play back that pre-record through speakers on set so the actor can follow along. It may also mean that the music editor is on set and ensuring perfect sync and dumping it into Logic or Pro Tools on set to ensure this before shooting is called for that day. In this case, it starts with meeting on it early and go over solutions as to how to make it work. Don't wait until you arrive on the set and argue with the lighting team while you drink your add-shot dirty-chai lattes that their lights get in the way of your mic placement on that violin, and don't be surprised if the director gives you a confused look if you ask for another 2 takes of that musical performance because it needs to sync to a pre-recorded track. The pre-prod meetings or some sort of coordination before shooting day should hash all that out. This is where it is decided that No, the real wind in DiCaprio's hair on the bow of the Titanic is more important than capturing the dialogue - the wind machine takes precedence, and it'll get handled with ADR.
That being said, sadly this is not normally the case today where the Sound Department gets full cooperation from each of the other departments on a shoot. However, this does happen sometimes and audio is given free reign! Some examples of this can be seen in the film Hurt Locker - they created a prop helmet to be able to capture the dialogue from the bomb suit in the most intense scenes of that movie. Per interviews I have seen, Tarantino has been known to re-light an entire scene if the production sound crew has difficulty getting close enough and achieving good tonality with their mics. Personally, I would love to see how the music was recorded for the film "Whiplash" - amazing performances caught on film and who knows how they did it? Good stuff. I wasn't at any moment thrown off by something out of sync in that movie - maybe I was too enthralled in the story.
Sorry for diverging, but I think your question is best answered with making sure you get your hands on the script early, going over with the departments before shooting how to get what you need, and hopefully the director is tracking enough with the entire process (production, editing, post, etc.) to make it happen with the least amount of headaches in post production.
