Is this a Service Desk project? If so, then yes, there is a simple way to do this. There is a built in Automation feature in Service Desk projects that you can use in order to create a custom rule that would send a notification when a comment is added, and you can then setup a IF condition that is something along the lines of status=closed.
Automating your Service Desk has more details of how this can work.
If this is not a service desk project, then automation isn't a native feature to these other Jira projects. I'm sure there is a way to do it, but it might be more easily configured through the use of a plugin to Jira.
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