Not exactly the same, but in Michael and Joanna's show at BADC a while back, she went down for a drop and somehow her heel caught on his shirt. She tore a gaping hole right through it. He played it off like "whatttt" while she acted like "come on let's get this show on the road!" It was actually one of the most memorable moments of the show.
I haven't been dropped... but I have been thrown by an over exuberant partner in a Cha Cha. It was supposed to be in place of a fan, and we worked on it in practice... and when it came time to get on the floor, it felt like he threw me about 10 feet.
Not dancing. I fell out of an ice-dance lift onto my bum once, though. My coach felt AWFUL even though it was really my fault (it was a lift where we were in dance hold with me going forward, him going backward and I had to "step up" with one hand on his shoulder and my ankle between his knees as the base. I botched the timing and there was really no way he could save it, but he still felt terrible even though I was fine.)