Izzy is the wife of the Riff of the Dimension of Rain and the technical member of the Resistance. She is the best at manipulating computers and helped get them all new identities as members of a police squad. She is also heavily addicted to 4U City's stimulant drugs and the 4U City coffee. (though she claims she is trying to cut back)
At some time in the past she and her dimension's Riff met, and she was able to make him come out of his shell and be more outgoing. They eventually married before he left to find Zoë. Izzy was absorbed into 4U City when it was created and was found by alt-Torg. Her skills with computers came in handy with tracking down Riff when he arrived and helped them secure new identities. She was a little disappointed when she found out that the Riff they found wasn't her's, this was compounded by Riff's behavior. It was also discovered soon after he arrived that Izzy was addicted to the 4U City coffee and the "uppers" drugs from the chemical vats. They've been slowly eating away at her physically and mentally (though the cleansing cocktail helps). Her growing problem is another thing that Riff is concerned about, because as her husband's dimensional duplicate, he feels he has to take care of her and do something about her problem.