When you downgrade from a paid plan to another paid plan the system redirects you to the credit card authorization system or PayPal to accept the new lower recurrent payment rate.
The recurrent payment for the old plan is automatically deleted.
When you downgrade form a paid plan to a free plan the recurrent payment for the old plan is automatically deleted and you will never be charged again unless you upgrade to a paid plan again.
All the previous links, settings, stats, and services will remain active unless the new plan does not provide those services.
If the new plan does not allow these services (i.e. Dedicated Domains or Personal URLs), all the links associated to those domains and URLs will be deleted.