All clients (Cases) remain in the database whether they have received assistance recently or don't ever return for services -- No action is needed on your part. However, if you wish you can add a new Demographic field called "CLIENT STATUS", or something similar, and includes the option "INACTIVE". You could then denote when a client leaves your services and mark them "INACTIVE."
see screenshot - https://simon.d.pr/i/fV4vhQ
If you are a network administrator, here are the steps to follow to do this:
Visit your [Admin] tab in the top-right corner
Click the [Demographics] sub-tab
Click [Add Demographic +] button
If you need to run a report on all "Active" cases, you can still do so. When you set up your report, click on "Filter by Demographic Profile Match" and select "CLIENT STATUS: None". see screenshot - https://simon.d.pr/i/4dusDh