If you break a string, of course, you can change rackets. But just as an aside, if it's a rec match I look forward to breaking a string and playing with it as long as I can. First of all to see how long it takes for my opponent(s) to figure it out and secondly to discover the weird things you can do with a stick that's progressively turning into a colander of macaroni.
I was practicing once with this hot (but dumb) chick and broke a string and she never noticed forty-five minutes afterwards; I heard she fell off her bike when she was a kid and hit her head. Just a few days ago I was serving on clay down in the desert and broke my gut (right in the center I'm proud to say) without warning--usually gut gives you plenty of warning and I can call the shot I'm gonna' break it on, but this time it caught me by surprise maybe because it was so hot out and the strings were cooking. I mentioned it (shouldn't have) and my partner (don't remember his name) said he had a spare (he came unusually well prepared to a club match). I said thanks and that I had one too and would get it on the change-over. I hit another serve and won my serve. No one else said anything (sometimes they go look at me like I'm crazy--I am) and insist I change rackets--I don't and keep playing until it's better to play with the butt end. I switched to my wet (synthetic string) racket on the change-over.
The trick is to play center court strategy because the strings will trampoline and the balls will sail. Try it sometime for grins and see what happens. You may be stuck on a desert island Club Med someday with no stinger around. Just doing my share to get the max out of endangered cat-gut, to preserve valuable resources and prevent climate change.
"...the human emotional system was not designed to endure the mental rigors of a tennis match." Dr. Allen Fox