Facilities and space stations are not given to factions in the form of datacards, they are simply just able to make them. (Meaning, that faction could not "assign" the ability to make a SY4 the same way they could "assign" the ability to build a ship or droids, someone from that faction would actually have to go out and build it wherever the customer wanted it.)
What happens then if the datacard is removed after production has started? Either through dissolution or being unassigned. I would presume it would continue, but would it just freeze until it is reassigned?
The datacard is needed to start production, it is not needed for production to continue once it's been started. When limited uses of the datacard have been assigned for instance starting production of 1 ship depletes those uses by 1 ship.