I have never experience a string that break in the middle of a performance, but, once when i had a recording for tv show, due to 'too many' lights on, and we were sweating all over, and which cause my A string to be out of tune, i couldn't tune it since the peg is loose.
I just play whatever i could play(but quite difficult without the A string), so i just act 'as if ' i am playing, but with the bow lightly over the string, but not making any sound, and i make sure my bowing is correct so that others won't know.
When i view the show on TV myself, ahah! That seems all right! it looks like i am really playing...because my fingerboard and fingers was blocked by the music stand...other people cannot see!
But that is my worse experience (so far

).