When attempting to remove an archive mailbox, the deletion never occurs. This happens whether the object is cloud-only or synced over via AAD Connect. Additionally, there is no litigation hold or in-place hold. If there is a retention policy set to all mailboxes, the mailbox has been excluded from that policy as well.
To correct the problem, there is an attribute on the cloud mailbox and cloud archive called ‘DelayHoldApplied’. Once that value is changed to ‘False’, the archive mailbox can be removed. This can be done either before the removal of the archive mailbox in the cloud-only scenario. In a synced account scenario, this change can be done prior to the removal of the archive of just after.
Upon research, this article explains the purpose of this attribute:
This parameter is available only in the cloud-based service. The RemoveDelayHoldApplied switch specifies whether to remove delay holds from the mailbox. You don’t need to specify a value with this switch. The removal of a hold from a mailbox is temporarily delayed to prevent the accidental purge of content that’s no longer affected by the hold. This temporary delay in the removal of the hold is known as a delay hold. To see the hold history on a mailbox, replace <MailboxIdentity> with the name, email address, or alias of the mailbox, and run this command: Export-MailboxDiagnosticLogs -Identity <MailboxIdentity> -ComponentName HoldTracking.