Ok, as someone who has been in virtually the exact situation as your GF, call a lawyer and confirm that it is legal to refuse the test.
I worked at a store, someone was stealing (hell I wasn't even in the shop the first few times it happened). After a couple of months the thief became more brazen and started stealing on shifts I was on. I suggested ways for the manager to fix the problem, but she ignored me. Eventually they created a list of ten suspects. We were told a telephonic polygraph test was being scheduled. I wrote up a legal letter explaining that I am doing this under duress (coz if I was the only one who didn't do it, it would make me look guilty). A friend of mine advised that I don't do it, but I told him that I wasn't guilty, and even though I'm nervous I shouldn't have anything to worry about.
Guess what happpened?
Machine picks me up as lying. They ask me to tell me the truth, I tell them the truth that I didn't bloody steal anything from them, and if they only listened to me we wouldn't be in this bloody situation. After trying to grind me down, they "accept" that I am telling the truth, and they legally can't fire me, but boy, did they make my life hell afterwards. A large amount of the staff somehow found out and I was basically treated like a criminal even though I did nothing wrong. I eventually found a new job and cut my ties with the place.
I had done some research and knew the machines can produce false positives, but didn't think I would. Legally, they cannot fire her based solely upon the polygraph test. Usually the cops use the polygraph test to get people to confess, by saying the machine said you are lying.
If I was you, get on the phone to a lawyer NOW.
P.S. There was a guy who was their main suspect, and whose shifts matched the exact pattern of the person stealing. He passed the polygraph test with flying colours.
