So, I work in live production, specifically in audio. With very, very few exceptions the mics themselves and the mic cables have no immediate redundancy other than someone being ready to deal with a problem should one occur (though if a lead vocalist is using a wireless mic, there may be a wired mic tucked away someplace on stage the talent can get to quickly if such an arrangement is practical.) The reality is that the mics aren't terribly prone to failure while in use (except in musical theatre, but that's a different lecture). Cables? Most of them, once plugged in and laid out aren't being touched or moved; they're also not likely to fail. There are exceptions of course, but most of those scenarios have been replaced with wireless anyway. For all sorts of reasons, anything critical on wireless will typically have some form of redundancy available.
In the pure analog days, all the mic inputs went to analog transformer isolated splits. One and only one console would provide phantom power for those mics and DI boxes (which convert the signal from instruments like electric guitars to a level and type useful for mixing consoles) that require an external power supply; typically this would be the monitor console. The remaining splits (however many required - would go to FOH audio (the PA), broadcast, multitrack recording etc...) so that each would get its own clean perfect copy of all signals that they could manipulate, process, and mix as required.
So, at that point, a failure of something with the PA for example would leave the broadcast or recording unaffected. Now, in terms of multitrack recording, there will often be yet another split and multiple recorders, DAW or other multitrack recording devices.
Things are only sometimes different today. Most shows/concerts (though not all) use digital consoles. Virtually all these consoles are designed with the idea that your inputs go to one set of analog to digital converters and the signal then gets split and distributed to the various systems digitally. This does happen sometimes, but at this point, I'm still seeing analog splits and the various systems using their own converters after the analog splits. This choice gets made for a variety of reasons including, but not exclusively, to maintain an increased level of redundancy (other reasons include negating the need for the various audio engineers to agree and decide which engineer gets control over the analog gain applied to each signal prior to the A/D converters and what that gain should be set to.) We tend to be a prickly, opinionated lot and wars have been started over less. It's kind of a miracle you got us all to agree to the mic selection.
So basically so long as the producers/promoters will pay for it, we incorporate as much redundancy as is technically practical and financially feasible in any place that is particularly prone to failure. Many top end consoles for example have two mix engines (the computer part of a digital console); if one fails, you can switch over near seamlessly to the other from the control surface (which at this point is pretty much a glorified USB keyboard and less likely to experience a failure than the mix engine).