No, it is not possible. All domains on the internet have to be renewed on a yearly basis. In case your domain has expired, it can be bought by any other person on the web. However, most domain providers ask you to buy a domain or renew it in a grace period. If you wish to renew your domain, you can do so, otherwise, you will lose control over your domain. You can verify your ownership of that domain by contacting the provider. Verification of ownership is a process where you make sure you still own the site.