The more open the draw, the more often this happens. With a more narrow draw, the bits get stuck in the airway and you have to do the pipe cleaner. Mostly, either way, it doesn't happen with most blends.
Unburnt tobacco I'll let slide, the flavor is not unfavorable. Toward the end of a bowl, however, if an ashy bit makes it through I'll grab it as quick as I can or spit depending upon my environment.
I find flakes don't have this problem, mostly because, you know, flake. Also, I'd be careful if I were you. That sort of thing can get one in trouble eventually.