When Unified Backlog is installed you may add a Triage Board to take Tasks in that may then be converted to Stories and added to your Agile Board's Backlog (Unified Backlog).
OOB, when the original task (e.g. Incident) is closed, the associated Story record which would be displayed in the Agile Story > Backlog, would be removed. This is expected behavior, as the thought process behind that implementation is that the life cycle of a story created out of triaging a record would be shorter than the lifecycle of the original record.
While this behavior is OOB, you may modify an OOB Script Include 'BacklogMetaDataService' to not hide Stories when their original tasks are no longer active.
- Navigate to System Definition > Script Includes
- In the "Name" column search for BacklogMetaDataService and go to the record
- Go to line 37 of the script
- Remove the portion: ^original_task.active=true
- Save/Update the Script Include
*Please note that modifications are suggestions and should always be done on sub-production first, as the above-explained behavior (in Description) is the current designed behavior.