The escape process of particles accelerated at supernova remnant (SNR) shocks is here studied with a phenomenological approach which allows to quantify its impact on the cosmic-ray (CR) spectrum observed on Earth, as well as on the gamma-ray spectral signatures emerging from these sources. Under the assumption that in the spatial region immediately outside of the remnant the diffusion coefficient is suppressed with respect to the average Galactic one, we show that a significant fraction of particles are still located inside the SNR long time after their nominal release from the acceleration region. This fact results into a gamma-ray spectrum arising from hadronic collisions that resembles a broken power law, similar to those observed in several middle-aged SNRs. Above the break, the spectral steepening is determined by the diffusion coefficient outside of the SNR and by the time dependence of maximum energy. The model of particles escape is also applied to electrons, including energy losses due to emission in radiation and magnetic fields of the region. Consequently, the comparison between the model prediction and broadband data allows to determine the model parameters which regulate both the energy-dependent escape process, as well as the particle propagation. We present the case of the Cygnus Loop SNR, where indeed the combination of radio and gamma-ray observations provides constraints on the efficiency of particle acceleration.