If the document is protected by a Label or Template, you can change the Usage Rights, Groups, and add new Users to existing Groups without needing re-applying the Label to the Document - There may be a short delay before the new permissions are active. If the document was protected by custom permissions then you'll need to re-apply the protection again.
To check if the document was protected by a Template or Custom Permission, you can use a PowerShell Get-AIPFileStatus PowerShell cmdlet.
For additional and detailed information, you can also take a look at Azure Information Protection FAQS - Data Protection
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