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The last decades have seen a burst of experimental platforms reaching the so-called strong-coupling regime, where quantum coherent effects dominate over incoherent processes such as dissipation and thermalization. This has allowed us to create highly nontrivial quantum states and put counterintuitive quantum-mechanical effects to test beyond the wildest expectations of the founding fathers of quantum physics. The strong-coupling regime comes with certain challenges though: the need for a large isolation makes it difficult to access the system for control or monitoring purposes. In this work we propose a way to access such systems through an engineered environment that does not compromise their strong-coupling effects. As a proof of principle, we apply the approach to the photon-blockade effect present in nonlinear resonators, but argue that the mechanism is quite universal. We also propose an architecture based on superconducting circuits where the required unconventional environment can be implemented, opening the way to the experimental analysis of our ideas.