I've deleted a post but have noticed that a search for a word in it's subject line will find the subject line link of the deleted post. If you click on this subject line link to see the entire message it gives you a file not found, as I would expect. Is there any way to delete the subject line or at least omit it from any searches a customer may perform? Thanks

Threads that are deleted are NOT removed from the search index automatically, in order to save CPU time.

You should rebuild the search index using the Index option in your UBB cpanel. That will remove the dead posts.