The authors present the possibility of obtaining perfect longitudinal wave absorption in a rod by the use of combination of point scatterers attached on its surface. Such a cluster of points is described as a matrix of point impedances, significantly impacting wave propagation in a rod. The problem is addressed analytically, by deriving formulas for non-symmetric reflection and absorption coefficients for the system. Later on, we provide theoretical examples of an extreme wave absorption for given impedances. Moreover we derived physical parameters of such a point impedance cluster (namely described with their masses m₀, stiffnesses κ and damping coefficients ν) that allows realization of extreme asymmetric wave propagation. Finally, we calculated conditions necessary for maximization of the extreme wave absorption in a wider frequency bandwidth.