After breaking their workstation (that it spawned with) the villager loses its job and when you bring it into the nether it gets the job that it spawned with. You can no longer trade with the villager even though it looks like it has a job, it cannot change jobs when other workstations are placed down, it basically becomes an unemployed green villager. I tried to do this in two worlds and the same thing happened.

UPDATE:
The problem was that they were not assigned to any bed, when you place a bed beside them they still remain the same but then you can place down a workstation and the bug is fixed.