If a non-admin user creates a (non-shared) feed that then breaks, cron sends the admin "A feed could not be found" messages, but the broken feed isn't visible in the Add/edit feeds list (Blocks > Remote RSS feeds > Manage all my feeds).

The capability block/rss_client:manageanyfeeds sounds like it should enable management of any feed, but in code only enables users to edit feeds with shared=1

It should be possible for a suitably powerful user to edit any feed on the site, to fix this - especially as feeds persist after users are deleted.