I can relate a story to you that shows SOME flexibility. There was a band in Cleveland called Wild Horses. Really popular. They were your basic cover band but they wrote one single, Funky Poodle, and it was a local hit. They were fronted by an old friend named Steve Jochim (who I have always called Poodle). A band I was in at the time played that song. One night Steve was in there just hanging out and I told the guys to start Funky Poodle but just keep looping the intro.
So we started it and I said "Where's Poodle at??" And I located him and pointed at him and then did the "come here" gesture to get him on stage, and we did his song.
But THAT was not an unknown quantity coming on stage to try to wing a song. I mean, he wrote the song he sang. Very different circumstance.