Two-dimensional electromagnetic cloaking devices with infinite optic constants at the inner boundary are investigated. Numerical simulations of this class of ideal cloak, performed with the transmission line modeling method, confirm the fundamental importance of such extreme values in the efficiency of the cloak in some situations. This is illustrated by using the concept of the anticloak, which was shown to be capable of defeating the non-ideal cloak. We numerically show that the presence of a layer with extreme constitutive parameters renders the anticloak unable to produce its effect. Furthermore, we propose a simple theoretical model that leads to the same conclusion if the cloak is slightly dissipative.