The permission of all saved searches can be managed by any user who has the appropriate permissions to modify the search (see: features available by role). Search Administrators, Compliance officers, and Administrators all have access to any saved search in the system. Exporter and Reviewer roles need to be granted explicit permission to a saved search in order to access the results.
Under the "Options" section of the search details page, managing the user access section enables administrators to provide access to users with the Exporter and Review roles. The actions the user is able to take on the search results is limited by their role.