Even without oscillation, interactions that conserve momentum can lose a varying amount of kinetic energy. Here's a trivial example, with linear momentum. Two objects of the same mass, with equal but opposite velocities collide. Momentum and kinetic energy is conserved if the objects end up with the same velocities as before, but each has reversed direction. But that's not the only way to conserve momentum - any kinetic energy is possible afterwards between these two cases. As before the amount of energy lost depends on how much the objects deform, and how much of that deformation is reversed after the collision.