The Purpose of the Ring of Ash
I now can explain the function of the ash rings that are shown. When the smoke monster kills Bram, it approaches him and then clearly stops. Bram stands his ground confidently. The camera then shows a ring of ash surrounding his feet. At this point the smoke monster is not attacking Bram. Then the smoke monster strikes the ground and causes some damage (there is clearly some rubble that falls because of the impact). Bram loses his balance and is shown to have fallen out of the circle. Then very quickly the smoke monster attacks Bram and presumably kills him.
The ring of ash is a shield from the smoke monster. This is why later the temple dwellers start to spread it around the temple, and why the Jacob’s cabin is surrounded in ash: to protect Jacob. The ring’s purpose is not to keep the smoke monster/MiB/Jacob’s Nemesis in because we see the smoke monster flying around the island attacking the Losties at many points in the early seasons. Ilana noticed upon arrival at Jacob’s cabin that the ring had been broken; therefore, Jacob left and went to the statue because his cabin was no longer shielded.
The purpose of the ring of ash is to shield whatever is inside of it from the smoke monster. What I do not understand is why Jacob needed protection from the smoke monster even though he apparently cannot kill him at all.