Emails you when a campaign that should be running flips into a non-serving state - Google calls this misconfigured or not eligible - and includes Google's own reason for it. It only fires on the change into that state, so it won't nag you about a campaign that's been off all along.
Defaults & settings
Trigger states - which campaign statuses count as stopped. By default, the two serious states Google reports: misconfigured and not eligible.
Limited - a softer "running, but held back" state; off by default because it's noisier.
Checks every 15 minutes; 7-day cooldown per campaign.
Example. A campaign's only ad group loses its last active ad, so Google flips the campaign to misconfigured. The email tells you the campaign and Google's stated reason, so the fix takes minutes instead of being discovered in next week's report.
Good to know. This rule covers a campaign-level stoppage. An account-wide stoppage (billing, suspension) is the job of Account went dark - the two together mean nothing can stop serving silently at either level.