Recent advances in deep neural networks (DNNs) have significantly improved various audio processing applications, including speech enhancement, synthesis, and hearing-aid algorithms. DNN-based closed-loop systems have gained popularity in these applications due to their robust performance and ability to adapt to diverse conditions. Despite their effectiveness, current DNN-based closed-loop systems often suffer from sound quality degradation caused by artifacts introduced by suboptimal sampling methods. To address this challenge, we introduce dCoNNear, a novel DNN architecture designed for seamless integration into closed-loop frameworks. This architecture specifically aims to prevent the generation of spurious artifacts-most notably tonal and aliasing artifacts arising from non-ideal sampling layers. We demonstrate the effectiveness of dCoNNear through a proof-of-principle example within a closed-loop framework that employs biophysically realistic models of auditory processing for both normal and hearing-impaired profiles to design personalized hearing-aid algorithms. We further validate the broader applicability and artifact-free performance of dCoNNear through speech-enhancement experiments, confirming its ability to improve perceptual sound quality without introducing architecture-induced artifacts. Our results show that dCoNNear not only accurately simulates all processing stages of existing non-DNN biophysical models but also significantly improves sound quality by eliminating audible artifacts in both hearing-aid and speech-enhancement applications. This study offers a robust, perceptually transparent closed-loop processing framework for high-fidelity audio applications.