quantum field theory - Feynman diagrams with classical apparatus on the perturbative region

In QFT, one usually simplifies the interaction between fields and classical apparatus (sources, detectors, etc.) by assuming the classical devices only interact with the asymptotic on-shell states

I'm interested in physical scenarios where such approximation would give incorrect results.

Conceivably one can put a logical or measurement device (which we can simplify as a bit or qubit state in some system) with enough coupling and/or proximity to a source such that one cannot assume that the device bit state must interact only via asymptotic states, in the computation of the Feynman diagram amplitudes