It's not like zero TBN will spell instant death to the engine, but at a theoretical TBN=0 there is no reserve alkalinity detected. So any acid by-products can have their way with metals sensitive to acid (free H+) corrosion in the presence of water. As mentioned this would be Fe alloys primarily.
What you'd see is corrosive/chemical wear of the softer alloys inside the engine. Specifically the Pb overlays on the main/rod bearings as well as any parts made of copper, brass or bronze. The harder metals would tend to be the least affected by a low TBN.