Inactive projects opion in the Reports section of display_options.php page defines whether or not to include inactive projects in the Reports dropdown control on the reports page for group managers. Inactive projects display option
At the time of this writing, this option is applied to users having view_reports or view_all_reports access right (Supervisor and higher roles). Regular User gets only assigned and currently active projects in there, while a Client gets both active and inactive projects that are relevant to them.
The Inactive projects option, when disabled, is intended to reduce clutter in the Report dropdown control and also load on server for Time Tracker groups that have a large number of inactive projects.