Auto-save HA log upon every Hassio/HassOS restart?

What I would like to accomplish is to have the Hassio startup process (including via HassOS boot) copy the current home_assistant.log to a local backup before starting Hassio . It’s OK that the original backup gets rewritten on each restart as it’s only needed for “what just happened” forensics if a restart occurred.

Why? I had a remote Hassio/HassOS RasPi3B+ system suddenly quit responding to both https and VPN/ssh access with no way to access the log file and pull the SD-card to see what killed it. (I do know it was highly unlikely to be due to a lack of space or memory).

A family member visited the remote site and power cycled the Pi and it restarted normally. Since the restart clears the home_assistant.log, I’m left clueless what the issue was. I may also add a smart plug to remotely power-cycle the Pi the next time it completely hangs.

Thanks for any advice if modifying the startup process is even possible on HassOS. If not, it’s a reasonable feature request, I suppose.