Say I am computer-unsavvy, or I tend to loose my computer, or it gets stolen a lot. Whatever the factors, I decide the risk of me holding my own bitcoins and losing them is higher than the risk of you defaulting. If this is true, then it does make sense to lend you the bitcoins at a negative interest rate.
That being said, I do not think it will ever come to this. My prediction is that the value of bitcoins will never rise strongly and consistently enough to justify a negative interest rate.
If you are wanting someone else to hold your money, you are not lending but storing or depositing. If, in such a circumstance, you would expect to be able to get back your bitcoins at no notice, interest would not be an issue but there would likely be some kind of fee you would have to pay for the service.
In truth, I can't see anyone ever lending at a negative interest rate. Regardless of the mathematics of the thing, you typically lend to get back more of what you're lending. Since the mathematics kinda-sorta make sense, it seems likely we are missing a piece of the puzzle.
What is the difference between giving somebody a loan or giving somebody a deposit? It is just a matter of semantics based on who is the larger party. Not all deposits are available on demand, such as CDs.
You lend to get more back than you would by just holding. Again, if just holding something is risky, the expected value might be lower than the expected value of a no-risk investment. The problem is, I do not think the risk of default will ever drop below the risk of lost coins. There are just no deposit takers who are trustworthy enough to be no-risk.