What you want can be easily accomplished. The tasks are under a particular Project. If you click on the gear like icon next to the Project name, click EDIT PROJECT, then go to Advanced Settings (scroll down). You get an option, Locked. Just lock the project.
Then the person who has been assigned the task will not be able to delete it.
Hope this helps !
Let me know if you have other issues
Great! I thought there's no option for that. Thanks so much. Appreciate the feedback.