Murtaugh will die in the final installment.If you dial 666 at the very end, he will rail at you until you leave.
Murtaugh is trying to save souls of all people from the ancient, powerful enemy named Entropy.A very, very long and crazy story... The mad, evil god named Entropy created humans to puppet them into slowly and painfully destroying the Earth and other ecosystems. The plan worked perfectly... except that a handful of privileged people gained Psychic Powers began to see the truth, sensing Entropy eating their souls and those of other living beings. While the lower class and other living beings died in tons by environmental destruction, starvation, resource scarcity, wars, diseases, and god-knows-what-else, the psychics moved to the hyperspace (where Entropy's influence is significantly reduced) to think of a solution. In the hyperspace, they learned how to defeat Entropy for good, but there wasn't enough energy to carry out the plan (Entropy's such a powerful entity). However, there was enough energy to perform a time travel, so that was what the psychics did. They left the Submachine in the hyperspace to store the memories (since there is no Ripple-Effect-Proof Memory going on) and to instruct them what to do to defeat Entropy. Hence, Submachine beamed a message into Murtaugh's brain, making him awaken his powers of travelling in and out from hyperspace earlier than the "first time around". There, Submachine led Murtaugh and his colleagues, including the player, to search for the data stored in it. The plan doesn't seem to be going smoothly, though, and Murtaugh is slowing losing his mind without apparent cause. And that is not to mention the possible Stable Time Loop that will continue the cycle again and again and again and again...
The subnet is a TARDIS...And it the sumachines have taken over, so to speak.
Murtaugh couldn't repair the damage he had caused in his native layer because--that's the layer where his arm is missing. Murtaugh's karma arm is stated to be his left arm spread across 7 layers, not all 8. The arm he's missing isn't the one in the timeless 8th layer, it's the one in the 3rd, taken by Shiva in tribute for his karma arm as mentioned in Murtaugh's notes. Thus Murtaugh couldn't repair the 3rd layer because in the 3rd he did not possess whatever karma arm powers he used to do so in the others.