This will not happen, once you let your domain expire, the registry change the nameservers in the domain so the domain will not point to our servers or to the server you were pointing the domain. Any services running in our servers or the pointed server for your domain will not work as the domain is not linked to that server. If anyone access you site, they will see a placeholder page by the registry or simply the known "Not found" page by your browser. If someone send you an email it will be rejected or bounced back to the sender as the domain is not pointing to the mailserver.
Once you renew your domain, the registry will change back the nameservers on it and point it again to the last nameservers (our nameservers or any nameserver you had on it), then after the DNS propagation time (usually between few minutes to 24-48hrs) any associated services (web page, email, etc.) to the domain will start working again.
For this reason we always recommend renew your domain before it expire, you lose no time renewing it early but you can avoid headaches doing it.
