I have not paid attention in a looong time and did not even vote (I forgot) but if there is a commited group of players I don't think the game needs to be shut down
I do not know about the bare minimum amount of players, but I'd say it is probably around 10 or so active players to staff all mandatory roles?
Assuming no Constitutional Amendment:
Game Moderator (3)
President
Vice President
Attorney General-Secretary of Internal Affairs (combined role)
Secretary of State
SoFE/RG (combined role)
Supreme Court (5)
Senators (18)
Lincoln Governor
LGC (3)
Fremont FM
Fremont Parliament (3)
Southern Prince
Southern Vice Prince
41. You could of course have some dual officeholders, shrink the Senate and/or SCOA and/or abolish the regions but this is the current base structure.