Is it possible to list all docker contianers with a restart policy set? I could inspect the running containers (How to quickly show policies of all docker containers), but what if one has been previously stopped, or has an on-failure policy and has completed successfully?

>Solution :

I could inspect the running containers (How to quickly show policies of all docker containers), but what if one has been previously stopped, or has an on-failure policy and has completed successfully?

Exactly, so do not stop at running containers – inspect all containers.

Just list all containers with that policy.

docker ps -a -q | xargs docker inspect | jq -r '.[] | select(.HostConfig.RestartPolicy.Name != "no") | .Name'

How does docker system prune work with this?

It does not work with this (?).

Will it skip the removal of any containers that are stopped, but have a restart policy set?

No, a stopped container is also removed. Observe the following terminal transcript:

$ docker run --restart always -d --name test alpine
7f22c1f1439b9a211ac85bf10b4da563aaa8f76a2229c290f1fceb0404ded2a8
kamil@leonidas /home/kamil
$ docker stop test
test
$ docker ps -a
CONTAINER ID   IMAGE          COMMAND        CREATED          STATUS                              PORTS     NAMES
7f22c1f1439b   alpine         "/bin/sh"      3 seconds ago    Exited (0) Less than a second ago             test
$ docker ps -a | grep test
7f22c1f1439b   alpine         "/bin/sh"      10 seconds ago   Exited (0) 7 seconds ago                test
$ yes y | docker system prune
WARNING! This will remove:
  - all stopped containers
  - all networks not used by at least one container
  - all dangling images
  - all dangling build cache

Are you sure you want to continue? [y/N] Deleted Containers:
7f22c1f1439b9a211ac85bf10b4da563aaa8f76a2229c290f1fceb0404ded2a8

Total reclaimed space: 41B
$ docker ps -a | grep test
/* empty */