After a domain name expires it will be available for everyone to register. We always send reminder emails to avoid the service interruption due to the loss of your domain name.
After the expiry date your domain stays reserved (for you to renew) for 30 to 90 days (depending from its extension) during which you can restore it paying and extra fee. If after this period you haven't renewed your domain name everyone will be able to register it.
In the case someone registers your domain name there is nothing you can do other than buying it back from the actual owner.