Yes, you can disable the "Edit" permission on the ticket on the Closed status. Without the Edit, you won't be able to create subtasks.
See http://www.j-tricks.com/tutorials/permissions-based-on-workflow-status for some examples on how to restrict permissions on workflow status.
We already have done that at the workflow level. Edit is not visible But Create SubTask button is visible. We need to hide that for the last status (Closed). We can still click on Create Sub Task when in Closed status and we get the next screen to enter things.
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