ANSWER: Nicotine is a toxic substance, and can be fatal in doses as low as 30 mg. It acts on a nerve receptor in the muscle and brain. It is an effective insecticide but is considered too dangerous to use for this purpose.
Nicotine is not a major carcinogen. Tobacco smoke is certainly full of carcinogens, but the nicotine itself is not.
Ideally, your girlfriend (whom I congratulate on stopping smoking) would stop the nicotine replacement usually in eight to 12 weeks after quitting smoking. However, there are some people who become psychologically dependent on the nicotine patch. In that case, you have to balance the health risks of the nicotine gum against the health risks of going back to smoking. The risks of the nicotine gum are small, and the health hazards of smoking are enormous. To me, if she feels that the risk of her smoking again is high, then it is safer to keep using the gum. If she feels pretty confident about not smoking again, she can try gradually switching to regular (sugar-free) gum, since it may be the gum sensation more than the nicotine she needs. The Food and Drug Administration is considering an indication for long-term nicotine use.