Happened to an acquaintance of mine a few years back, at Bessy Beck fishery.
He had wound his line in, but left the fly on the waters edge, a cruising trout took it while he was talking to me.

Luckily for him BB is a small fishery and not too deep, the weight of the reel made the butt sink, and the rod top was sticking out of the water being dragged around by, we think a decent rainbow.
It was comical to watch, he was panicking, and I had a small dry fly on, but another chap close by came along and cast his heavy lure over the line and we managed to pull the line in, the fish was still on at this point.
My friend was so relieved, he grabbed the rod, and as he did so, the fish came off.

His face was a picture.
S.