The Marshal would have lived through his injuries if not shot by Sawyer and then killed by Jack.
DHARMA chose the Island for it's experiments because of its pre-existing healing properties.
The healing properties explain why so many people survived a massive plane crash with only minor injuries. Everyone that didn't die on impact was miraculously and instantly healed by the Island.
The Island will refrain from the use of its healing powers if someone is using it for bad purposes. For example, Locke had trouble walking when he led Boone out to the plane wreck where Boone was injured despite having been warned about Boone's injury through a vision.
The Island only heals good people. This explains why Ben was not healed of his spinal tumor but Locke and Rose were healed of their ailments, and why some people fall ill to the Sickness while others stay perfectly healthy.
The explanation that Tom gave to Michael on why he could not kill himself is because the Island won't let him as he has work to do. This might apply here - the Island only heals those who have work still to do and therefore need to survive. When it allows people to heal normally, it is because they do not need to be healed immediately.
The Island heals people off the island as well. Obviously, the island won't let Michael or Jack die because they still have work to do. This is an indication that the island can effect the outside world to some extent. It's possible that the island healed Carole Littleton and Diane Janssen too. Claire's mother was said to have very little chance of surviving and was in a coma for several years but she miraculously came out of her coma. Also, Kate's mother became very ill with cancer and the doctors had given her 6 months to live for the past 4 years.
Claire was probably very hesitant to abandon Aaron and she probably took into consideration the psychic's warning of how no one else can raise Aaron. In addition, Claire may have still felt resentful towards Christian for abandoning her. As compensation or incentive to leave Aaron and stay with Christian, Jacob/Island healed Carole for Claire. This mirrors how Jacob supposedly healed Rachel from cancer in return for Juliet to stay on the Island.
The Island has healing properties that Jacob can somehow control. The Island/Jacob heals, protects and saves people who serve some sort of purpose in the master plan.
All attempts to kill Locke and Michael have failed because the Island/Jacob still needs them. Ben shot Locke; Locke almost shot himself; Jack tried to shoot Locke; Michael tried to shoot himself; Keamy tried to shoot Michael. Each time they lived because they still have work to do.
Jack got sick because the Island/Jacob doesn't need him anymore. The Island/Jacob now has Claire and she is to replace Jack in some way. On the same day when Jack started to feel pain, Claire meets Christian (presumably working for Jacob) who takes her away. Likewise, Ben got sick because the Island/Jacob doesn't need him anymore. The Island/Jacob now has Locke who has replaced Ben as protector of the Island. Ben discovered the tumor a day before Locke arrived on the Island.
After watching the last episode, I now believe the Island/Jacob allowed Jack to get sick so as to keep him on the Island - Jack still has work to do.
Someone needs to die in order for someone else to be healed. For example - Shannon was shot and Sawyer healed, many died on the plane and Locke, Rose and Jin healed.
Locke seems to have reoccurring paralysis. This may be some rare disease, something that had been pressing on his spinal nerves after the fall suddenly released by the impact of the plane crash.
Jin: Even people with fertility issues are able to procreate sometimes. Maybe just getting away from his very stressful occupation helped.
The Island or the fact of surviving a plane crash could have "lifted the spirits" of the survivors. Many turned faithful or have some other spiritual experience (see List of Recurring Themes:Religion and Ideologies). The most miraculous healing was invisible (Locke, Rose, Jin) and were all based on illnesses that are known to be sometimes susceptible to self-healing by willpower/faith.
The island heals those who still have work to do or are special. You have to be extremely special to heal from a very serious injury.
As Jacob said, the island wipes everyone's past clean. Everyone gets a fresh start on the island. This includes ailments and injuries: Locke's back, Rose's cancer, and Faraday's memory. This does not mean that a person cannot get sick once they are on the island. They do experience a quick recovery from any ailments on the island.
Both physical and psychological healing
On the island, people are not only healed physically, but also psychologically, which is relevant for a few of the Losties. Charlie manages to get the self-control to overcome his heroin addition ("The Moth"). On the island, Hugo was generally fine without heavy medication until his relationship with Libby was about to begin and the temporary stress of his personal insecurities caused a momentary relapse. A short while after he leaves ("I was happy too for a while" he tells Jack in "Something Nice Back Home"), Hugo starts hallucinating a best friend again, this time, Charlie as opposed to Dave and ends up back in Santa Rosa Mental Health Institute. Likewise, on the island Jack is kept busy with one crisis after another, as Sarah and he himself mentions several times, Jack is most comfortable when there is a problem to fix ("Man of Science, Man of Faith"). This is why Ben knows that Jack will one day wish to return to the island (King of the Castle). After he gets back to the outside world, Jack's issues reemerge. He and Kate become a couple after leaving the island (Something Nice Back Home), she now a single mother, and Jack steps in to be the dad. But Jack's grief about his father's death returns; he thinks he sees Christian in St. Sebastian Hospital ("Something Nice Back Home"), where they used to work together ("All the Best Cowboys Have Daddy Issues"). In response, Jack starts taking medication (which he later abuses in"Through the Looking Glass, Part 1"), and restarts the binge drinking he began before flight 815 in the bar where he met Ana Lucia ("Pilot, Part 1"). In the end, he recreates the issues from his last relationship. Jack accuses Kate of being unfaithful to him (Something Nice Back Home), just like he accused Sarah of cheating on him with Christian ("Pilot, Part 1"). Later it is implied that he has been repeatedly calling Kate against her wishes ("Through the Looking Glass, Part 1") like he stalked Sarah in a previous episode. He continues his downhill slide, becoming suicidal ("Through the Looking Glass, Part 1"). But ultimately, the island may take him back after all - preventing him from killing himself by presenting a fiery car crash and another chance to fix something, just like it did for Michael ("Meet Kevin Johnson").