We make heavy use of relationships on our CiviCRM implementations to record a variety of situations: volunteer relations between an organitzation and a volunteer, grants concessions relations between an organitzation and a user beneficiary, etc.
Start and End Dates allows us to limit the time period in which the relationship is valid. Unfortunately there is no way to do a search of all the relationships that were active during a given period. See detailed discusion here.
A first approach would be able to search for empty dates as can be done in Relationship Reports. See how here
A second and more accurate solution would incorporate an optional search field to appear only when you select the status of the relationship Active or Inactive. Then this field allows you to filter the date range for which the relationship was active or inactive, depending on the case.