Jennifer Gale is the wife of the real Henry Gale, according to the note on the $20 bill that was left behind by him.
Information from Ben
Jennifer's maiden name was Murphy. She supposedly died three weeks previous to the events in "One of Them" of a fever which might have been the sickness. "It started as a fever. After two days she was delirious. Then she died."
Information from the Twenty Dollar Bill
She is likely to be alive, either in the real world, or on the Island.