FFXI is as most of us understand, pretty cheap to maintain, so I agree, unlikely we'll see a shutdown threat until server populations hit critical levels. (i.e. like less then 100 players each, which none of them are close to even now.)
SE definitely does handle it's MMO's very differently.
FFXIV 1.0 would have shut down completely in the first year of operation if almost any other company was running it, they would not have in a million years spent the money to remake it. That was a brave and dedicated move by SE, and it turns out to have worked, XIV is more popular then most MMO's on the market. Plus, how many other MMO's run their games with populations so low and not shut them down? FFXI is a profit machine still, it's future is safe for awhile yet.
I think, they'll take big steps to try and breath life back into FFXI, now that XIV is launched and set, long before they'd ever consider a shut down.
This means: ports to new systems (PS4 would be ideal, and easy to port to and highest install base of this generation, vita would give nice mobile capability but low population, 3DS or Wii U would be neat for dual screens and space saving, and esp with SE ammibos!!! I'll take prishe^^), graphic overhauls to appeal to wider audiences, and new expansions.
I don't think F2P is in the cards, SE has said not a chance several times, and even avoided it with XIV, I don't think for a moment it would, esp not still turning a profit. Plus a cash shop would take more work to implement then it would give back and have limited options due to the engines limitations, and buying currency as some mentioned would be pay to win and that never goes well, because as was said, who wouldn't just buy a cat's eye, or ampules or tokens and skip all the hard stuff?
Whatever happens, I just hope FFXI's core stays as it was designed to be.
That's why we are all here, and not in XIV.
Plus...
FFXI is my home^^
And I know it's the same for many others who keep coming back, or keep playing, several of my friends, and my partner included. And I'd bet it means a lot to a lot of the staff at SE too, esp those who worked/work on it.
