Exploring a more than 70 years old idea about the minimization of the spectral abscissa of linear functional differential equations, a series of recent works highlighted the insights that multiple spectral values may bring in the characterization of the decay rate for the solution of such dynamical systems. In fact, it has been shown that a spectral value of sufficiently high multiplicity tends to be dominant, in what is now known as the multiplicity-induced-dominancy (MID) property. When it is valid, this property can be remarkably helpful in the control of dynamical systems governed by functional differential equations or even some classes of partial differential equations. Beyond its simplicity, what sets it from other control methods is the valuable quantitative advantage it provides by prescribing the exact solution's decay rate. Since then, many works have been dedicated to studying the extent of the MID as well as its use in practical control applications. In this paper, apart from the extension of the MID property to difference functional equations with multiple delays, we study the case when the MID fails. In fact, despite the invalidity of the MID property, we emphasize the interest of forcing a spectral value multiplicity to derive a sharp estimate of the corresponding rightmost spectral value. To demonstrate the effectiveness of the proposed methodology, we consider the stabilization problem of the wave equation with an auto-regressive boundary feedback. By using an appropriate finite element modeling, a numerical simulation of the boundary control for the wave equation case is performed to illustrate these results through the example of vibrations' control of a long drill pipe submitted to a shock-like disturbance. The time responses show the effectiveness of the proposed approach and mainly that the decay rate can be arbitrarily selected.