If members have the ability to cancel their subscriptions, pay attention to any balance due (i.e. their cash account balance.) It is good practice to monitor canceled subs via Customers & Partners / CSA Subscriptions / Canceled on green menu on left. The default view sorts the most recent cancels to the top--Note the column labeled Canceled (date).
IF a member owes money there will be a $ in the far left column labeled Status. Barring a previous arrangement, bill the member right away using the Bill From Cash button in the member's cash account.
The first step of subscription cancellations made by admin should be to check and see if there is a balance due.