Board Thread:Questions and Answers/@comment-44935929-20200126205016/@comment-123.231.124.142-20200127123223

He's not truly alive. But yeah, a portion of his consciousness remains in the Blue Rose Sword. This can be attributed to 1) His multiple instances of using the Perfect Weapon Control, which is mentioned in the LN (not sure about the anime) as being very dependent on your memories to perform incarnation 2) The way that he even fused with his own sword to fight Quinella.

Again, he's not alive. There's a scene where Higa is on the Ocean Turtle monitoring Kirito's mind and he finds Eugeo's consciousness, but notes that it's coming from the Underworld component (called the Main Visualiser) that's responsible for storing objects, but not the LightCube Cluster, which stores Underworldian souls. Basically, since memories and objects have the same data format in the Underworld (it's previously mentioned that the Main Visualiser is responsible for Incarnation by utilising people's memories), while Eugeo's soul went on to deletion, his memories remained as an object of sorts.