The game does have a stalemate timer - at least in Skirmish mode, that is indeed a possibility. I don't know what happens to units left on the Strategy map if a stalemate occurs.
At the moment I do not really agree with the population growing after depletion, that is the entire point of the limited population system, but I haven't had a chance to play with people yet and experience how such a stalemate feels.
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This is only tangentially related, but after a battle on the Strategy map, the population pool for that country will be depleted, which is a really nice touch. But it seems to bounce back really, really fast. After the turn's end, the population for a country is displayed as two numbers - a white one, plus an addition in green, which is how many the population has increased since the battle's end.
It seems that the population boosts back up too quickly - there isn't even one full turn without a battle and suddenly is almost back up to where it started from. I think it should take longer for populations to return to normal. I like the idea that repeated battles in a single country could drastically change how it plays because there are fewer and fewer people left. It might even be interesting to get down to 0 population so that the country is just a battlefield and all your resources are the troops you brought and the few you can scavenge from selling buildings (recruiting the staff of that building).
