You can achieve this my creating different workflows (e.g. one for bugs and one for stories). In the Bugs Workflow you leave it as it is, and the Stories Workflow you can set properties on the steps as per this blog post in order to remove the permission to delete the issues.
That is, you'd need to add a jira.permission.delete.denied = denied property to all the steps in the Stories Workflow as per this documentation. Alternatively, you can use jira.permission.delete.group = jira-administrators for example so that only admins can delete issues.
It's a bit of work, but it's certainly possible. :)
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