You could do as Lukasz Lysik suggests, and have a field that serves as a flag for "deleted" rows, filtering them out when you don't want them showing up. I've used that in a number of applications.
An alternate suggestion would be to add an extra status assignment if there's a pre-existing status code. For example, in a class attendance app we use internally an attendance record could be "Imported", "Registered", "Completed", "Incomplete", etc.* - we added a "Deleted" option for times where there are unintentional duplicates. That way we have a record and we're not just throwing a new column at the problem.
*That is the display name for a numeric code used behind the scenes. Just clarifying. :)