It turned out instance had uptime for over a year, many application releases were installed, /var/lib/docker/devicemapper folder contained hundreds of items that apparently refer to older abandoned containers.

I saw the process of eternal reading all this data while dockerd -D command that runs docker interactively for debugging.

I removed /var/lib/docker and /var/run/docker and re-installed docker and containers on my box, the problem was resolved.

Feels like I need a script that would periodically remove obsolete items from docker internals.