Why does the caregiver calendar still show shifts after I made the client inactive?

Making a client inactive does NOT remove the schedules from the client or from the caregiver calendar.  

You need to go to Scheduling>Delete Bulk Schedules, 

and then select the client and the date range to delete.

 Use the check boxes to select all, and then click Delete.

Once the schedules have been deleted, you can change the client status to inactive.