by lithy
Tagged for same spoilers as above.[o]It definitely stays at zero because in the Game End steps, it says if a city would lose and gain a population, the population stays the same.
This is important because a city at population 1 with both a plague cube and supply center does not drop to 0 (thus triggering any Population 0 action) and then recover to 1. It just stays at 1.
As for the permanent supply center, I think I agree, it was built during the preceding game, so it can be made permanent.
In theory a city with a permanent supply center could lose population from Hollow Men multiple times and end up at 0 and then in the next game would get a supply center during setup and if not infected during that game (which could only happen from a plague outbreak I think) would be raised to 1 at the game end if the supply center was still there (I think it could be moved in theory although my memory of the rules there are fuzzy, not sure if I am mixing them up with research station rules from regular Pandemic.)[/o]
Further spoiler than above for OP to check
[o]You mention Bunkers but your spoiler tag only goes as late as September, might want to remove that or separate it out, I forget when those first appear. [/o]