If you measure income as change in net worth minus expenditures, it could go below zero. That might not be an appropriate definition in all cases, but, for example if you incur debts without acquiring an offsetting benefit (maybe by being compelled to pay damages to someone for something you did that you didn't derive much or any value from, like causing an accident?), it might be reasonable to say that you had negative income. Or maybe due to capital losses -- you own something that gets stolen or destroyed or damaged, or whose market value falls a lot.

(That doesn't mean that it will follow a Gaussian distribution, just that it could be defined in a way where it makes sense that it can sometimes be negative.)