fall before me and cry out in pain! farewell!After leaving the Oracle Knights of the Order of Lorelei, Gelda Nebilim moved to Keterburg and opened up a school there for the local children. Among her students were Jade, Dist, Nephry, and Peony. Despite being a rather troubled child (to put it lightly), Jade admired the Professor; while he could do fonic artes that even adults couldn't manage, he still couldn't use the Seven Fonon, unlike Nebilim. Nephry also mentions that Nebilim helped Jade understand what it meant for living things to die, but she never goes into detail.
Nebilim was apparently a kind and devoted teacher, as Dist still wishes to reunite with her and Peony named one of his rappigs "Gelda." But the Professor met an untimely end. Jade couldn't accept the fact that he wasn't able to use the Seventh Fonon, and one day, he tried applying the Seventh Fonon to himself, resulting in disaster. We see firsthand what happens when one who can't use the Seven Fonon attempts to use it with Mohs, who turns into a giant monster and undergoes "neural contamination." When Jade made his attempt, he created an explosion that set Professor Nebilim's house on fire. The Professor was near death, but he and Dist brought her to the edge of town and attempted to make a replica of her. The original Professor died while the replica was nothing like her original self. It was a monster, with dangerous abilities in battle. She would ultimately escape Keterburg and become known as the "serial fonist killer" after wiping out even an entire company of fonists. The monster was eventually sealed away at Mt. Roneal.
The death of Nebilim signified two major things for Jade. First, it was a moment when he had lost control of himself; he let his curiosity get the better of him and he ended up killing someone close to him. Jade later vows to never let himself lose control again. Second, it was an indication that replicas are not merely replacements. The replica Nebilim didn't have the thoughts, memories, and especially not the personality of his teacher. Jade tells Luke that he wants to beg Nebilim's forgiveness, but says that, "a replica cannot forgive me." Nebilim's death signified the fact that that Jade couldn't comprehend "what it means to die." Though he and Dist apparently made a promise to later revive the Professor, Jade says he no longer wishes to do so; though Nephry doubts this, Jade's obvious detest of living replication probably means that sentiment was true.
As an optional sidequest in the game, you can take on a search for the "Planetary Fonic Arte." It's revealed through the sidequest that Professor Nebilim was researching a fonic arte that could bring down "the mass of a planet" onto an opponent for Fon Master Evenos, Ion's predecessor. The arte supposedly required a series of "catalysts" in the form of weapons imbued with the power of Rem (light) and Shadow (darkness). After gathering the required weapons, the party ventures to Mt. Roneal, where they find a fonic glyph in a remote crag. They meet Dist, who reveals that Nebilim's replica, the serial fonist killer, was sealed away there. As a replica created using fonic artes, Nebilim was made with the First through Sixth Fonons, unlike Luke who is made up of solely Seventh Fonons. The process somehow results in missing fonons (causing mental instability), and Nebilim's replica states that she needs the First and the Sixth, Rem and Shadow. The catalysts could provide her with those fonons and make her "perfect." But the party fights and defeats her before she can gain that power. One thing is strange, though; you'd think that Jade would have realized that the search for the catalysts would lead them to Nebilim's replica. Even Dist knew that. But perhaps Jade did know, and wanted to use the strength of the party in order to put Nebilim to rest. But that's only speculation.