Can the coefficient of friction be negative?

yeah it can be negative but this is not the most common phenomena , friction is reduced by smoothening the surface of the body if two extremely somoothened bodies are slided over each other then you would expect that they should have been moving very smoothly but the actual thing happeining is entirely different , even though the bodies are smooth enough to avoid friction as both the are of same composition adhesive forces (force of attraction between similar molecules) dominates and thus act as frictional force resisting the motion between them