To answer the last bit; when there are no more improvements on the tile, the unit would automatically move to a tile with an improvement, if within its range, and pillage that. The turn it moved, seeing as it doesn't get any supplies through either supply lines or through pillaging, it would incur a health penalty. When there are absolutely no improvements left within a reasonable area (let's say, when there are no more adjacent improvements), then every single turn, a health penalty would apply:
One question that hasn't been answered yet (IIRC) is what the effect will be on units that have no supply? I would suggest that some parameter be established effecting their strength. Say, a -20% strength modifier for every turn they are without supply, max-ing out at 80%. Or perhaps an exponential, or sinusoidal, modifier on their actual health, whereby they lose health each turn that they do not have supply, in the function (where y = percentage of original health (0≤y≤1), and x = number of turns (0≤x≤10):
y = cos ([∏x]/20)
So that after 10 turns of no supply, the unit dies.
From
this thread.
This would be a more realistic representation, IMO. I mean, history shows that if you don't supply your troops, then they might not fight for you, but they aren't going to fight against you, or suddenly become barbarians. Mutiny is a much more realistic option.
Also something I forgot to mention before- I think that units should be able to go for 1 turn without any ill effects other than a hit to health. Realistically, units will tolerate a short term loss of supplies without mutinying. Two or three turns without supplies, though, and the mutiny could kick in.
Now, as for the first bit of your above post, well, I think the supply system should extent to
all units. That makes sense, after all. Even barbarians need supplies. They are just more likely to pillage for them. So, if we consider that they would need supplies, then units becoming barbarians would, if anything, reduce their chance of gaining supply. And then there is the whole thing again about the allegiance of troops, and the fact that historically speaking, units do not switch sides because they don't have supply. They might mutiny, but they don't often (actually, I can't think of any examples) switch sides, especially when the other side cannot assure supply.