When you are made redundant, whether through formal dismissal or because a temporary contract ends naturally, your employer will need to supply the Employment Office (SEPE/INEM) with a ´certificado de empresa´ stating all data relevant to your termination of your employment. They will send this electronically, but you can ask and have the right to receive a copy. This certificate is essential for your application for unemployment benefits.
You can also check yourself, online, whether your employer has sent the certificate, but you need either a digital certificate or a CL@VE to access the online office of SEPE for that. THIS LINK will lead you to access to the certificate (the button to the right), to check the data your employer has supplied, and you can also apply for a copy of the certificate.
If your employer has not sent off the certificate or won3t give you a copy, don’t worry, just make sure you make your appointment to claim unemployment benefits within the window of 15 days after your contract ended. At the SEPE/INEM office they will have you sign a form stating that your employer has not provided you with a copy of the certificate and they will contact him about it for you.
Guide about the Certificado de Empresa (in Spanish) to be downloaded from the same link as provided above, the second pdf-link at the top of the page.
Edited with missing links replaced.