In a market economy with strong property rights, complete resource depletion is extremely unlikely because prices telegraph in advance the information that the resource is becoming scarce. But what I'm saying is that even in a
non-market economy something similar can happen. Suppose the resource is food. When there's a big herd of dumb animals on the land it might not be worth anyone's while to try fishing instead. As the animals get fewer and smarter, it gets harder to get enough to eat; that is an incentive for individuals or families to try fishing or farming or moving away even
if there's no trade or prices or futures market.
Losing land to sea level rise - if it happens - happens so slowly and incrementally that there's plenty of time to move elsewhere or build levees or put things up on stilts. On a timescale of decades and centuries, things fall down and break; when you rebuild you do it a bit further inland or somewhere else.
We might be having problems because an ecologist's definition of "resources" and "consumption" is different from an economist's; I tend towards the latter. I fear that if we listen to the ecologists we might inadvertently create the very scarcity they fear.
(Matt Ridley briefly discussed the difference between the two in a WSJ article this week: http://online.wsj.com/news/articles/SB1000142405270230427990... )