Well, a thousand blocks can be managed in just a few minutes real time, so not that big a deal. Yeah, pick a direction and RUN!
If the spawn point has a lot of land, we should go with it. If it's on a tiny island, we should respawn with a new map. Perhaps we will know by then? Hell, I don't know.
As far as fencing is concerned, we have geo-fencing.
Check your coordinates. If you're at +1000, dig away!