The Law of conservation of Mechanical Energy states that in a closed system with no non-conservative forces acting, the energy of the system will always remain constant. This makes sense for an elastic collision where Mechanical energy is conserved. However, if an inelastic or completely inelastic collision takes places in a closed system with no dissipative forces acting on it, how is mechanical energy not conserved?
Energy is conserved in inelastic collisions. Bulk kinetic energy is not conserved.
The sources I learned from never introduced a "Law of conservation of Mechanical Energy". I assume it applies in a restricted mechanics where thermalization is disallowed and all energy must be expressed in terms of macroscopic coordinates.
In that case the energy lost from (or added to) the kinetic channel must be hiding in strain potentials of some kind (elastic potential energy or some non-linear generalization).