I have done this in the Beta. The next highest position simply gets promoted to guildmaster, or if there is no one else in the guild, the guild is simply disbanded. This may have changed in the retail release, but that's doubtful, especially considering this is the same thing other games do.
I do not know what would happen if you skipped a few subscription payments, but I would think in that case the guild would continue on as is, just as it would while you were logged off.
I don't think we know the answer to that question yet; it'd be nice to get an answer from Zenimax on that.
My guess would be that the group goes leaderless. If any of the second tier members has sufficient access, they can continue running the guild... but I suspect a guild leader that just drops off the planet orphans their guild.