"B" for "Because" crap happens
Don't freak out. Stay calm.
If your strap pops and you have nothing to repair it with, be gutsy--rip off the other strap and go strapless like the diva you are.
If you brought your fast-fix kit, dig into your reserves for some safety pins and pin that strap to your dress 'til the cows come home.
If a seam has popped, drag a loyal girlfriend to the ladies' room and ask her to help sew you back up.
If the tear is irreparable, use the wrap. Tie the scarf around your waist in a bow to hide midriff rips. No matter how badly you manage to tear your dress, there is probably some way of covering the damage enough to continue partying. And remember that no prom disaster can kill you. You will make it through this embarrassment.
Handle it with humor and self-assurance. Laugh and say, "Ugh! Darn Ikea clothing." Everyone loves a clown.