My ending analysis.

According to Ellone - The Final Fantasy Wiki

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The Final Fantasy VIII Ultimania explains that Ellone's ability to connect to the mind of another is the same kind of process as when a person junctions a Guardian Force; one's consciousness can't be connected to another without an intermediary with a special ability — a Guardian Force, Ellone herself, or the Junction Machine Ellone.

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Honestly, I don't even remember if this was talked about in-game or not. Of course, this doesn't answer what the origin of her power is, but I thought it was worth posting for people who didn't know the how of it.

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Originally Posted by Wolf Kanno

I feel that what most likely happens if a Sorceress dies is that they basically become a mindless zombie propelled by magic, to seek out a new host. Ultimecia didn't exactly seem all together when she gave Edea her powers.

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That's the impression that I got. They are forced to wander in agony until the Sorceress Power leaves their body to a new host. It is an interesting concept. It's a shame that the game didn't really play with the idea of how mysterious and foreign the concept of a Sorceress was. I remember feeling like the game just kind of threw the term out there and everyone was familiar with the lore except for the player. It kind of diminishes the effect of Ultimecia giving her speed in Deling City.