They can reject the transfer, the reason TUPE was introduced was to protect workers rights for situations just like this.
See above. You can reject the transfer if the company you're leaving will offer you a job. It doesn't apply to me, and i don't want it to as i'm joing a better company. In Rangers case it would appear not to apply as the old company doesn't exist. The resignation aspect is a grey area. It's simple for the likes of us who can leave a job with a months notice, but footballers are contracted for years.