Next-Chipmunk17's journey

I need some advice about a strange situation my fiancé is in. He interviewed for a job at a well-known retail chain and was told they would send him an offer after a background check. A few weeks later, the background check was still pending, and he hadn't received an official offer. However, the retailer called him and asked if he could start training, which he did, even though he hadn't received any formal offer yet. Now, he's been working there for two weeks, has received a uniform, and has a monthly schedule, but still no offer and no payroll. They assured him he would be paid for the time worked, but HR keeps saying the offer is on the way. He really likes the job and his co-workers, but this situation feels uncomfortable. He has a shift coming up on Saturday, and we're wondering if he should tell them he can't work another shift until he has a formal offer. He quit his previous job for this position, and we really need the paycheck, but I'm concerned about the legality and ethics of this whole situation. Any advice would be greatly appreciated!