There is a previous discussion describing the settings on JIRA Email This Issue plugin, which you can view here.
Apart from that, you can also achieve this by installing the Auto transition Listener which is shipped with JIRA Toolkit plugin. This listener will listen for the particular event (e.g. Issue Commented) on an issue then performs a transition (in this case reopen).
For anyone wondering:
PLEASE NOTE: This is currently not configurable in JIRA cloud, as the required Listener functionality of the JIRA Toolkit Plugin is part of the Restricted Functions in JIRA Cloud
There is a feature request to add the ability to access this in Cloud instances here:
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