A price can go negative for a physical thing which requires upkeep, but I don't see how a coin which imposes no obligations on an owner who just chooses to walk away, can have a negative price?

Oil went negative in the same way the price of my trash is negative: more of it was being produced than people wanted to buy, but the producer had to get rid of it because they couldn't stop production. As another commenter said, you can just walk away from a digital asset, so this isn't a problem. I can't walk away from my trash.