Swallowing a braces wire is usually not a cause for panic, as the wire will likely pass through your system safely:
How it happens: The human stomach and digestive tract have enough acidity to dissolve small pieces of metal within minutes.
How long it takes: The remaining piece will be excreted in a day or so.
What to do: You can eat high fiber foods like corn and bread to help the process.
When to seek medical attention: You should seek immediate medical attention if you experience difficulty breathing or chest pain. In extremely rare cases, you could accidentally inhale the bracket and it end up in your lungs. In this case, you should treat it immediately.