Can an employee whose employment does not transfer claim unfair dismissal under TUPE?

Yes. An employee does not have to work in the transferring part of the business in order to be protected by TUPE from unfair dismissal, as long as the reason for the dismissal is the transfer. However, the more distant the link between the dismissal and the transfer, the harder it will be to establish that the reason for the dismissal was the transfer, and not some other reason.