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 "Inactive Status", or something similar, and includes the option "Inactive". You could then denote when a client leaves your services and mark them "Inactive."
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 "Inactive Status: None".