Docker stopped working on Debian VM after host machine's drive filled up completely

I’m trying to run Docker on Debian 9.9. It’s a locally hosted virtual machine using VirtualBox 6.0.8. I installed Docker normally, and got the expected result from docker run hello-world. Then I ran a docker pull command and accidentally filled up the host machine’s disk drive.

After freeing up space and rebooting the machine, Docker gave the following error whenever I tried to start hello-world:

docker: Error response from daemon: cgroups: cannot find cgroup mount destination: unknown.

Troubleshooting I’ve already tried:

I tried the solution offered in this comment, and got mount: none is already mounted or <dir> busy for each command.

I decided to uninstall and reinstall Docker, but ran into more issues.
If the Docker daemon was running, apt purge docker-ce gave no errors, but left the daemon as a stuck process, and skipped any directories that were currently being used by the daemon. If the Docker daemon wasn’t running, apt purge docker-ce.
I ended up editing the uninstall script to remove the lines that shut down the daemon and replace them with exit 0 to get it to uninstall. After uninstalling, find | grep docker returned no results.
After rebooting to be safe and then reinstalling Docker with apt-get install docker-ce, I still get the same error.

I am out of ideas and my Google-fu isn’t strong enough to find an answer.