What do we suppose eventually became of Kull? Pastiches of the character are relatively few in comparison to Conan, and none have ever touched on his final days. I know there was a story in Marvel's Savage Sword of Conan where Conan, Red Sonja and Kull time travelled centuries after Kull's time, just before the Great Cataclysm, and found that Kull's legacy was that his own name was now the official title of the ruler of Valusia, but that's about it.
But otherwise, he lived as a king and at some point he died. From what Kings of the Night said, sounds like he lived out his life (compared to what we find out about Bran in Dark Man). Then again details may get hazy after 100,000 years. Current writers would probably succumb to the temptation of having him wiped out during the Great Cataclysm, but from what Howard wrote in Hyborian Age, it took place long after Kull's era.
I would say Kull had many more adventures and his alliance with the Picts was strong throughout his reign (the Picts still have the gem Kull gave Brule after 100,000 years in Bran's time) but I don't think REH gave any solid clues as to Kull's ultimate fate. Pure speculation here but perhaps Kull got summoned by the jewel into a far future time and never came back (I wonder what might happen if the Bell of Morni was rung by a future Gonar bearing the gem that Kull gave Brule). Perhaps off topic but check out Conan the Barbarian issue 68 for more of Kull's time travelling exploits, the plot was concerned a sorcerer who uses a formulae from the Book of Skelos to summon Kull and the Black Legion into the Hyborian Age in a bid to use them to take over the world. You also get a damn good Kull vs Conan scrap that ends in a draw (I have a feeling Conan would have won if went on longer though).