Simulating open quantum systems on quantum computers is challenging because dissipative dynamics are nonunitary, whereas gate-based quantum algorithms are typically built from unitary operations. Conventional approaches can overcome this mismatch by embedding nonunitary processes into enlarged unitary circuits, often with ancillary-qubit and gate overhead. In this work, we propose an alternative perspective in which we selectively preserve the physical noise to emulate nonunitary channels. More specifically, we present a partial encoding algorithm that iteratively leverages intrinsic noise to mimic the dynamics of a target open-system. We benchmark the convergence of this algorithm against the dissipative exciton transport Hamiltonian and retrieve their dynamics. By utilizing intrinsic hardware noise to emulate the target nonunitary dynamics, this approach avoids the dual overhead of error-correcting that noise and using ancillary qubits to re-introduce nonunitarity. This significantly reduces both qubit requirements and physical fidelity thresholds, paving the way for more efficient techniques to simulate open quantum systems on quantum computers.