Last year on a late night arrival in F, had an FA swap my coat for someone else's (very similar) and vv. They didn't turn the lights up, so I didn't notice. Fortunately he had a paper BP in his coat, so I was able to have a phone agent track him down and arrange for us to mail each other our coats.

I was lucky, since my coat had a stack of business cards I'd received at a conference in one of the pockets.

I agree with leaving a business card in anything you're not wearing during your trip. Of course now when I put my coat on I look for my business card to be sure it's mine.