If I were a Jedi, this would happen to me

At first I was gonna say no, but now that I think about it I've never seen an active light saber fall.......

But they have been thrown. I imagine a Jedi could turn it off with the force though.

True, Yoda did throw his light saber through the chest of a clone. He then proceeded to jump atop said clone and brutally rip his saber out of his chest. What a badass.

It depends on how the jedi/sith designed it.