The founders are showing a negative ownership stake! Can this really happen?

Well, no, not exactly but this is really for conceptual illustration purposes. For this to have happened, the founding team would have to destroy significant value in the company after raising money; and while this doesn't mean that you have to write the venture a check, it very likely means that you will be in danger of losing your job.

In reality, when this happens there will be a restructuring of othe company and if the board of directors still believes in the founding team they will be issued enough shares (or options) to motivate them to turn the ship around. In any case, we recommend trying to avoid this situation.