Coated laminates arise from sequential lamination, where an initial laminate consisting of a core and a coating material is repeatedly embedded into the coating with varying normals and volume fractions. For non-degenerate core and coating materials, explicit formulas for the effective conductivity and stiffness are known [1]. We focus on coated laminates with a degenerate core, namely insulating or infinitely conducting phases in thermal conductivity, and pores or rigid phases in linear elasticity. Motivated by empirical observations in the context of Deep Material Networks [2], we show that, provided the coating material is non-degenerate and the lamination sequence is sufficiently large, the effective properties of such coated laminates become non-degenerate. This result extends existing results for specific settings, such as rigid core fiber suspensions [3], to a more general framework. We derive necessary and sufficient conditions for non-degeneracy in thermal conduction and linear elasticity and illustrate the theoretical results with computational examples. REFERENCES [1] G. W. Milton, The Theory of Composites, Cambridge, Cambridge University Press, 2002. [2] S. Gajek, M. Schneider, T. B¨ohlke, On the micromechanics of deep material networks, Journal of the Mechanics and Physics of Solids, Vol. 142, pp. 103984, 2020. [3] B. Sterr, S. Gajek, A. Hrymak, M. Schneider, T. B¨ohlke, Deep material networks for fiber suspensions with infinite material contrast, International Journal for Numerical Methods in Engineering, Vol. 126, pp. e70014, 2025.