You can certainly use Automation For Jira to send an email when the status changes (which obviously would affect the count). Here is some more information for Automation if you are not familiar:
There are two types of automation:
Automation Basics: https://www.atlassian.com/software/jira/guides/expand-jira/automation
You can do this via global rules to apply to all projects also. You'll need to be a Jira Admin/Site Admin, go to Jira Settings > System > Automation Rules (left-hand menu).
For more on using Automation For Jira see these help pages.
Jira Automation Template Library to help get you started quickly:
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