When a written contract is not renewed, it becomes a contract "at will": that is, the terms, other than duration, of the prior contract remain in effect, but either party may terminate the agreement and relationship at any time on notice. So you don't have to keep working for them if you don't want, but you may keep working if you choose; they don't have to keep employing you, but can do so if they want; and you cannot force them to sign a new contract or a renwal--rather, your only recourse would be to stop working for them, if that's what you want.