Is there a way to terminate a task outside of the process which created the task

Check out the Task Smart Services Plugin and see if it will handle your case:
forum.appian.com/.../summary

You can use "Set External PV" smart service. which takes two things
1. active process id (where your task is present) and 2. target PV which you want to update.
Update that PV with true using the smart service and use that PV in task exception.
when the PV is true the task exception will execute and connect it to terminate node.

Hope this works in your case...