You can still access the tree and add to it. However, you can not access any new documents. The documents you tied to your tree previously cannot be accessed. For example, if you connected a death certificate, that fact will still be there, but you can't access the actual certificate. You can download documents to your own computer before the free trial ends.
Ancestry can keep the tree around forever until you remove it. If you don't want others to view your tree without your permission, make it private.