  The end of supernova remnant (SNR) evolution is characterized by a so-called
"radiative" stage, in which efficient cooling of the hot bubble inside the
forward shock slows expansion, leading to eventual shock breakup. Understanding
SNR evolution at this stage is vital for predicting feedback in galaxies, since
SNRs are expected to deposit their energy and momentum into the interstellar
medium at the ends of their lives. A key prediction of SNR evolutionary models
is the formation at the onset of the radiative stage of a cold, dense shell
behind the forward shock. However, searches for these shells via their neutral
hydrogen emission have had limited success. We instead introduce an independent
observational signal of shell formation arising from the interaction between
nonthermal particles accelerated by the SNR forward shock (cosmic rays) and the
dense shell. Using a semi-analytic model of particle acceleration based on
state-of-the-art simulations coupled with a high-resolution hydrodynamic model
of SNR evolution, we predict the nonthermal emission that arises from this
interaction. We demonstrate that the onset of the radiative stage leads to
nonthermal signatures from radio to $\gamma$-rays, including radio and
$\gamma$-ray brightening by nearly two orders of magnitude. Such a signature
may be detectable with current instruments, and will be resolvable with the
next generation of gamma-ray telescopes (namely, the Cherenkov Telescope
Array).
