No, friction cannot be negative, and the coefficient of friction cannot be negative either.
Friction is a force that opposes the relative motion of two surfaces in contact. It is defined as a vector quantity that always acts in the direction opposite to the movement or impending movement. Since the force of friction serves to resist motion, it is inherently a non-negative quantity.
The coefficient of friction (μ) is a dimensionless number that represents the ratio of the force of friction between two bodies to the normal force pressing them together. The coefficient of friction can take values from 0 to a positive infinite figure but not below zero. A negative coefficient would imply that friction aids the motion rather than opposes it, which contradicts the fundamental nature of friction.
In specific conditions such as when analyzing forces in a system, you might see mathematical representations that could imply negative values; however, that does not correlate to the actual physical coefficient of friction or the frictional force behaving as negative.
In summary, both friction as a physical phenomenon and the coefficient of friction as a measure are always non-negative.