In this article I will explain why Jacob isn't dead, and why he's protecting the Island.
First, let's go over Jacob's death scene. Ben stabs Jacob. Jacob tells MIB, "they're coming". And MIB pushes Jacob into the fire pit. However the next day when Ilana is inside the tomb, there is no phyical remain of Jacob in the pit. There is only ash, and she scoops it up, and puts it in a bag.
I highly doubt that the fire was hot enough to cremate Jacob's body. So that leaves us with the problem of the missing body, or atleast it's skeletal remains.
Secondly, let's recall that Walt was able to teleport, or atleast astrally project. Remember, in episode, "three minutes", Ms. Klugh asked Michael, "Has Walt ever been somewhere he wasn't meant to be?".
Let's assume Jacob has similar powers to Walt. Thus let us speculate that Jacob teleported out of the fire pit, but remains extremely injured, hence why his powers are greatly diminished, and why the temple water turned murky.
Let us recall that Sun couldn't get pregnant because of her scarred fallopian tube. Furthemore, it wasn't until she landed on the Island, and as a result of its healing properties, was she able to get pregnant. The result was Ji Yeon. Therefore, if Sun never found the Island, Ji Yeon would never exist.
Let us assume that in a future timeline Aaron, whom I believe to be Jacob, and Ji Yeon fall in love, and somehow (Fate) get stranded on the Island. Once stranded on the Island, he discovers Faraday's diary. And in that future timeline Jacob starts skipping through time. Let us futher assume he skips to the very deep Island past and causes the MIB to come to the Island; much like Desmond caused the passengers of flight 815 fates towards the Island. In the very deep past the MIB plots the destruction of the Island. Jacob realizes that without the Island, his love, Ji-Yeon, will not be there, if he returns to his present timeline. Thus his ostinate need to protect the Island until the Losties come, and Ji Yeon is conceived.
It also explains why he can speak Korean, since his wife, Ji Yeon is Korean.
The conjecture that Aaron/Jacob is from the future trapped in the past explains why the MIB can't kill Jacob.
The temporal contradiciton/rule is this:
Jacob caused the MIB to come to the Island. If Jacob is killed, the MIB would never have been brought to the Island.
The MIB is still on the Island. Thus the MIB hasn't been able to kill Jacob.
The key to this theory is to shift from the Losties timeline as the dominant timeline to a future timeline, which the Lostie timeline is a derivative of.