[FFmpeg-user] resume encoding live HLS stream?

[dan]

I've googled to death but I can't find anything but other people
asking for this.

Specifically, I want to encode an HLS 'kit' live and if the ffmpeg
process gets stopped, I want to restart it but continue on with file
numbering and keep the old chunks.

A few examples:
A) ffmpeg segfaults because of some wacket error in the input, I'd
like it to start back up (in a while true; or via systemd script etc)
and preserve the old files in the m3u8 instead of starting over.
B) There is a power outage and when the system comes back up and
starts the ffmpeg script I don't want to erase all the history.

I plan to keep about 72 hours if the live stream available and allow
users to jump into the history at any point via js in the browser,
which I have working but every now and then something gets reset and I
have to start from scratch.

Is this possible with ffmpeg and/or is it something on the wish list?