I believe that the supplies they are using on the island are for the most part all the leftovers from the original dharma participants. The original inhabitants abandoned, or were removed from their quarters years ago, and all of the abandoned technology is from the 70's....
I believe the future "eutopian" society that grew from the research on the island has encountered a problem in the future. They must go back and correct their mistakes, or they might perish. They need medical knowledge desperately now, they eliminated it many years ago because it was no longer needed. (pefect bio engineered humans do not get sick) I am not suggesting that the survivors are trapped in a time warp etc. I am suggesting that the island has a portal that the others from the future are using. Perhaps they cannot bring inanimate objects (including clothes) But, they can communicate to a degree and arrange for food drops from an outside source. If you can manipulate time travel you can manipulate people and events to your benefit. I am thinking that the second island is either a ruse/mirage or that both islands are in the same general area of the magnetic field and would share the healing benefits.
Yeah, I know...... on the edge of psychotic aren't I?...lol