You don't actually own a domain name in the way that you own your physical property. You have the exclusive right to it for the period of registration, after that it returns to the registrar and can be taken by somebody else.
So, if the registration hasn't expired then you still "own" it. If it has then you have lost it.
you don't have to purchase a domain name from bravenet even
you can purchase a domain name from godaddy.com even and get hosting at another place
but as long as you have the domain and hosting it is under your control if your domain expires and you don't renew it then it will become available for someone else to purchase and host somewhere as was said