My PhD research has a negative outcome -- how can I still graduate with it?
Conditions Under-which Fancy Algorithm Has Inflated Error Properties by A. Student. Journal of Science and The Doing Of It. 2017.

This would be a perfectly acceptable paper, and one which should appear in the literature. If you can, correcting said algorithm so it does not do so would be a bonus, but not necessary. Also, it's slightly late for you, but one should always ask when embarking on a thesis/dissertation project "What happens if the answer is "No"?"