I don't have a grammar rule for this one, but I do have a related comment: keep them to a minimum. I get really annoyed when a major character is always trailing off, or hesitating.
I see it a lot in romance manuscripts, in particular, which may be why I'm so sensitive to the topic. A minor character who's a trailing-off wimp, I can live with, b/c I'm supposed to find him annoying and weak, but a protagonist or antagonist who's so weak he/she can't speak in firm sentences drives me up a wall. Unless, of course, it happens once or twice at moments of extreme distress, and then it's against a backdrop of usual competence. Just as long as it's not all the time.
Okay, I'll be quiet now. But it's a pet peeve of mine. Just cannot read stories where people are trailing off constantly. Makes me want to slap them upside the head and tell them to grow a backbone or a brain or SOMETHING.
JD