Orphaned ticket (Incident, Problem, Change etc) is a ticket which has no workable task and thus cannot be worked on normally. At the same time, ticket still may have characteristics of an open ticket - status is not Closed, completion percentage is not at 100%, ticket may have a task that is not workable or there may be items in the database that usually accomplany an open ticket (notably, messages).
There are two sides to the problem of orphaned tickets:
Orphaned tickets showing up in reports. For example, tickets that are supposed to be closed still show up in reports as open.
Orphaned tickets still being processed internally. There are internal processes that do check things periodically on open tickets, this should be avoided for tickets that are orphaned and no longer worked to avoid unnecessary performance hit.
There is a number of reasons a ticket can malfunction and become orphaned. This is not an extensive list but most examples of most common circumstances:
Certain known issues
Environmental issues (especially on SQL Server)
Changing tasks in a ticket manually (or automatically with a custom Workflow project)
There are projects available in Connect to close ServiceDesk tickets forcefully. Tickets will not be deleted and they will still be in the system but these will be marked as closed as well as be functionally closed (i.e. no further checks or processing will be done on these).
Please note that these projects are not supported by Symantec Technical Support and having a backup of the ServiceDesk database is strongly recommended before using these.