The exchange 2016 rule does not take effect

Hi @yanhaowen

Thank you for posting your question in Microsoft Q&A. 

We understand that your mail rule not work as your expected, the mailbox quota condition is letting those outbound emails bypass your transport rule and send mail to external. We are glad to assist you this part. 

In my perspective , this could be caused by rules are automatically executed for new messages but it's not applied to the existing emails that are already in your Inbox. When the mailbox used by the system reaches its quota limit, emails are queued in the Outbox instead of being sent. The rule to delete emails sent to external recipients might not applied to emails stuck in the Outbox. That is why, when you manually delete emails to free up space, the queued emails are sent without the rule being enforced. 

If it possible, you could try to increase the quota limit. 

Increasing the quota can help prevent issues when it's full and ensure your current email is not delivered to the outbox. 

You could refer via: Configure storage quotas for a mailbox | Microsoft Learn 

However, as the moderators in this community have limited resources to check the backend information, and to get the fast and better assistance we requested for it. To resolve this quickly and effectively, Microsoft’s support team will need to step in. A technical support engineer can perform a remote session to investigate the situation, verify the backend configurations, and run any necessary synchronization tools to resolve the problem. If the issue requires further attention, they can escalate it to a specialized team for deeper analysis.      

Reference: Get support - Microsoft 365 admin | Microsoft Learn  

If you have any additional concern, feel free to comment below. I be more than happy to assist.

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System messages are not subject to mail flow rules generally:

https://learn.microsoft.com/en-us/exchange/security-and-compliance/mail-flow-rules/mail-flow-rules#system-generated-messages