I do have this happen from time-to-time. So I've sorted how toavoid broken strings (I use a nylon pick, avoid using multiple capos, I ofund string that rarely break) - but I always have multuple instruments on-hand; just-in-case.

I have had to talk to the audience through a string change, on occaiosn. It ain;t the end of the world. People are patient, and it doesn;t take too long top change a string ....

BUT in general, it is a pain-in-the-as* when strings break during a set.