Yes, If you're overburdened, you can keep moving (but no jumping or running) until you run out of stamina. Then you just stop. As you've already noted, your stamina does not return and won't as long as you are overburdened. You're not sleeping. You just have zero energy and will stay that way until you dump the extra weight. Your stuff will just lay there for a long, long time. Once your stamina is replenished, you can pick the stuff back up and continue, but you'll run out of stamina and stop moving again. You can do this over and over again until you get where you're going. Actually, this is what carts are for.