You're right about non-cash additions. I was confusing this with an enterprise showing a loss (especially for tax purposes) despite a positive cash flow. The classic example would be residential real estate, where depreciation can cause a net loss despite the landlord receiving enough rent to pay mortgage/property tax/maintenance. This is why in the U.S. there are rules that limit current deductions on the tax return for passive losses.

So I would think the "other way" from profitable/no cash flow is loss/with cash flow.