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Integrated photonic systems provide a flexible platform where artificial lattices can be engineered in a reconfigurable fashion. Here, we show that one-dimensional photonic arrays with engineered losses allow the realization of topological excitations stemming from non-Hermiticity and bulk mode criticality. We show that a generalized modulation of the local photonic losses allows the creation of topological modes both in the presence of periodicity and even in the quasiperiodic regime. We demonstrate that a localization transition of all the bulk photonic modes can be engineered in the presence of a quasiperiodic loss modulation, and we further demonstrate that such a transition can be created in the presence of both resonance frequency modulation and loss modulation. We finally address the robustness of this phenomenology to the presence of next to the nearest neighbor couplings and disorder in the emergence of criticality and topological modes. Our results put forward a strategy to engineer topology and criticality solely from engineered losses in a photonic system, establishing a potential platform to study the impact of nonlinearities in topological and critical photonic matter.