IMO Google has the right approach with "advance directive" options, while respecting owner's absolute right to not permit others to take over their account if that's what they prefer.

For GIO,  "sunset" actions would be triggered if no owner posts to the list, or sends email to +owner (which might be monitored by other moderators), or logs into groups.io for a specified number of days.

I think the following options are enough (each with its own sunset period).  Multiple actions of the same kind would be permitted:

Just Notify: Send an email to arbitrary recipients (possibly including the list) with a user-specified message.  The timer continues ticking.

Discussion: Owner might privately give their password to someone who could take over.  Or they just want someone to remind them if needed and if they are still alive/capable of acting.   The timer keeps ticking if there are any other actions with longer timeouts, such as Delete.

Add Owner: Add specified email addresses as Owner(s) (upgrading existing subscribers, otherwise just waiting for that email to subscribe).   The timer keeps ticking.

Discussion: It would be up to a new Owner to delete the old Owner if appropriate, i.e. if they were dead.

Change Settings:  Change any of the things under "Settings".   The implementation probably would run a special copy of the Settings dialog to collect the info and then save the results, to be slammed into the real settings when the timeout occurs.

Discussion: This is the most general way for Owners to arrange to transform a group after they are gone, for example by changing the "Description" to indicate the group is 'legacy' or 'archived'.  They might also enable all Members to download archives if not previously allowed, disable posting except by Moderators, etc.

Freeze: Sugar for "Change Settings" to prevent all further activity (no posts, no editing, etc.) and to install a new group "Description". 

Discussion: If an Owner later appears, they could, of course, revert the settings and resume normal operation.  Paid accounts would automatically revert to "free" status if payments stopped being made, thereby reducing storage limits, and at that point files and attachments might be deleted, but not message bodies. 

Permanently Delete: Delete the group and all archived content, optionally sending a specified "Epilog" message to the list (this might be implemented internally with a "Notify" event a few days before the actual group is deleted).

Discussion: Any owner always has the absolute right to delete the group without notice; this is just a way to do so "posthumously".

GIO Enforced Delete:   All groups would have a non-disablable "Permanently Delete" action with some distant timeout, e.g. 5 years, subject to acceleration (with advance notice) by group.io if applied equally to all groups.

Discussion: Necessary to protect groups.io from an unlimited obligation to provide free resources to store, index, and serve dead groups.

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