If the due date is set on the issue, you can query issues that have a due date in jql, and save the search as a filter, then you'd want to subscribe to this filter and set the cadence for how often the email will send. Since it's based on duedate I'd say once a day should suffice.
If you have a step in your workflow where you would like JIRA to send an email notification, you may be able to rig something if you have JIRA Suite Utilities and/or ScriptRunner Plug-ins. (Im not sure which does what since we installed them both before our initial rollout) Id have to research further how - and it would depend on your configuration- but Im pretty confident it is possible with these plugins.
