Just wait. You can’t control when the background process runs. It can be bumped because some other service processes take precedence. The goal is to run weekly, but it might take longer.

I am testing this process in our dev environment before going live with it. I read from another contributor that the process should send a message within 24 hours of a group becoming ownerless. Your article states the process runs weekly. I made a group ownerless a few days ago by soft-deleting the owner account, but have not yet received a message to any of the test members. I just made a separate group ownerless by hard-deleting a separate owner account and I’m waiting for a result. I am using a Team-backed Microsoft 365 group to send the messages assuming that fulfills the 365 group or user mailbox requirement of the policy config.

Aside from the audit log, are you aware of any other way to see if the process is actually running and failing somewhere? Or should I just be patient and assume it will eventually get to a point where it does its weekly run?

Have you logged a call with Microsoft Support? They can check what’s going on in the tenant… we can’t!

Here MS says that Shared mailboxes are not supported. I was confused too.

https://learn.microsoft.com/en-us/microsoft-365/admin/create-groups/ownerless-groups-teams?view=o365-worldwide#:~:text=Note%20that%20shared%20mailboxes%20are%20not%20supported.%20The%20sender%20must%20be%20either%20a%20user%20mailbox%20or%20a%20group%20mailbox.

The email is generated by Microsoft. You’d have to ask them. I suspect not.

No. Maybe this will help: https://office365itpros.com/2018/11/15/finding-inactive-distribution-lists/