Jennifer Gale is the significant other, possibly the wife, of the real Henry Gale, according to the note on the $20 bill that was left behind by him. ("Dave")
Information from Ben
Posing as Henry Gale under the captivity of the survivors, Ben offered some information about Jennifer to Sayid while under interrogation. Ben claimed her maiden name was Murphy, and that they met at the University of Minnesota. She had supposedly died three weeks earlier of a fever. "It started as a fever. After two days she was delirious. Then she died." ("One of Them")
Information from the twenty dollar bill
She is likely to be alive, either in the outside world, or on the Island.