At the premiere of her new movie I Am Number Four, Dianna Agron started out on the red carpet wearing a pretty baroque updo, but as she walked on, it appeared to come tumbling down. It's possible she switched up the style mid-red carpet. However, if it was simply a slip of a few strands, Dianna handled it beautifully. Instead of freaking out, she just let her hair go, allowing it to cascade into a wavy ponytail.
In situations where your hair is falling out, your best bet is to let it do what it wants to do, try to make the new style look as polished and intentional as you can, and readjust a few bobby pins as needed. Most importantly, though, stay calm and confident. A big smile can help you carry off almost anything.