The literature on growing network models, exemplified by the preferential attachment model and the copying model, has followed an exponential growth in the last few years. In many real-life scenarios, however, the adding of new nodes and edges is not an exogenous process, but involves inheritance and sharing of the local environment of the existing ones. In this paper, we develop a mathematical framework to analytically and numerically study the percolation properties of the random networks with proliferation. We compare random attack (RA) and localized attack (LA) on benchmark models, including Erdős–Rényi (ER) networks, random regular (RR) networks, and scale-free (SF) networks, with proliferation mechanism. Our results highlight the nonmonotonic connections with robustness and growth, and unravel an intriguing opposite effect for RA and LA. In particular, it is shown that unbalanced proliferation enhances robustness to RA while it mitigates robustness to LA, both independent of the network degree distribution.