In Soul Eater, the Immortal Clan is a group of people, like the name suggests, who are immortal. Their ability to live for hundreds of years suggests that many clan members still exist but so far, only two members has been seen in the entirety of Soul Eater. The remaining members were either killed or taken into custody.
Those within the immortal clan are werewolves, in which means they possess the ability to transform between a human and werewolf and are immortal and able to heal instantly from physical attacks. However, the only way of killing an immortal is attacks from the Hunt-Slash series or beheading.