First of all, all Broadway shows fall under union agreements and regulations.
Any musical theatre piece is indeed a gruelling rehearsal process. Usually anywhere between 6 to 12 months of rehearsal, that's 8 hours a day, 6 days a week. Not including fittings for costumes, props, etc and not including the enourmous amount of tech calls and rehearsals.
For the most part, every majour role will have a specifed understudy. Someone else in the cast that will know and can do the role as well, in case the principal is ill or unable to perform (yes, sometimes performers get a day off, unlike as us Stage Managers who do not have understudies :)).
Also, there are positions called "Swings." These are performers who learn up to 5 different tracks in the show (principal, chorus and other). They can be put in on a moments notice in case of emergency or illness. This is also why Opera for example only performs every other day, and never two shows in a row.
There are also many things that performers are encourage to do while in the midst of a long run. Drink lots of water, warm up properly to avoid injury and just generally take care of themselves.
As per union regulations, there are also things that are provided for their use: a massage therapist, physiotherapists, lung and sinus doctors, etc. Also, there is a maximum number of shows allowed in a week, and a maximum number of shows allowed in a day (ie. you can not do 4 shows back to back, which would be 2 days of 2 shows).
Truth is however, that the run of the show is the easy part. Only having to work for a max 4 hours a day is a blessed relief after a gruesome 12 month rehearsal period of 10 hour days.
No job in theatre is easy, there is always work to do outside of the show as well. At least performers get to go home after the show and don't have to come back until the next performance. The rest of us get to take care of tech notes, costume and prop notes and all sorts of reports and paperwork, after we run the show. :)