You can copy files out and then back into a container (even when the container is stopped) with the docker cp $cont_name:/path/in/container /path/on/host to copy out and then docker cp /path/on/host $cont_name:/path/in/container.
You can copy files out and then back into a container (even when the container is stopped) with the docker cp $cont_name:/path/in/container /path/on/host to copy out and then docker cp /path/on/host $cont_name:/path/in/container.