I know that the Synolog Docker UI for instance allows to change every parameter of a stopped container. My guess is that they destroy the old container and create a new one using the new configuration, while doing some dirty magic with implicitly created volumes (at the end those a named volumes with a random name).
There is a docker update [OPTIONS] CONTAINER [CONTAINER...]command, though it is restricted to updating cpu, blockdevice and memory related contraints. The command docker container update [OPTIONS] CONTAINER [CONTAINER...] is identical.