Jennifer Gale is the presumed 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, they met at the University of Minnesota. 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 outside world, or on the Island.