Yes, it is possible to have active/inactive or any other project status for a phase, irrespective of what the main or parent project has. You can change the Status of the phase to Active/Inactive manually from the list view or by going into the detailed view of each phase.
If you want to change the status of multiple projects to Inactive, we recommend using the Actions > Batch Update option from the Projects list view. Check CORE Help Center for details.