One cool thing about having Bitcoin is that they cannot go below zero.
Discussion
You could conceivably borrow Bitcoin like you can borrow any other currency. A Bitcoin lending market hasn't emerged yet but there's nothing preventing that from happening.
Some exchanges let you short Bitcoin or so I hear which is pretty much that. Bitcoin's extreme volatility is a pretty big obstacle to borrowing it.
Sure you can always dig your own hole. And in contrast to real world holes they are not limited to the earth‘s core.