Sir Fabian was a knight of Eleum Loyce. He led the Knights of Eleum Loyce straight into the depths of Chaos to exterminate the terrible things that dwelled there but not one of the selfless Knights of Eleum Loyce returned.
We are not given a time period for this event and it is therefore left to speculation. We know that Eleum Loyce existed before the Ivory King and that it gave birth to the Old Chaos, which the Ivory King eventually subdued, to an extent. Because the description of Sir Fabian's deeds are so similar to those of the Ivory King's it could mean a number of things.
One explanation is that the Ivory King is Sir Fabian. We know that the Ivory King was the highest ranking knight in Forossa so he would have been a 'Sir' and that he led his Knights into Chaos. However this explanation seems unlikely because the Ivory Crown specifically states that the Ivory King's name had been forgotten, and it also contradicts our knowledge from the Loyce Soul that at least some of the Knights who followed the Ivory King into the Old Chaos did return, though they lost their sense of self.
Alternatively, it could be describing an attempt made on subduing the Old Chaos under the Ivory King's rule by one of the Ivory King's knights. But this does not match what we know of the King's nature; a selfless man who would always be first to lead his warriors into battle.
Finally, the above could be describing events from before the Ivory King's arrival. We know that the Old Chaos caused the people of Eleum Loyce to flee, but why would they give up their city without a fight? Perhaps because their strongest warriors had been bested by the Old Chaos. The Ivory Straight Sword description also makes special mention of the fact that ivory is native to the land of Eleum Loyce. Why bother to do this unless it had some significance to the rest of the description? It may have been a clue that Sir Fabian too was native to Eleum Loyce and therefore wielded a weapon native to the land. The fact that the weapon is made from the soul of Aava, the Ivory King's pet may contradict this theory in some way, but honestly, we don't know where the King's pets came from, as they may have been inherited from the abandoned land.