Kulkarvek was the only Urgal king. After his death, his body lay in state in the Barrows of Anghelm. Of the warnings that the Eldunari gave Murtagh and Thorn for their travels in the north, this was the first. The Quote from Umaroth, who spoke for the Eldunari brought from Vroengard, is as follows:
"We know much of the difficulties you have faced, Thorn and Murtagh, for we have watched you from afar, even as we have watched Eragon and Saphira. There are many things we would teach you once you are ready, but until then, we will tell you this: in your wanderings, avoid the barrows of Anghelm, where the one and only Urgal king, Kulkarvek, lies in state... Do this and, unless you are greatly unfortunate, you shall not encounter danger beyond your ability to master."
This could mean that, with all the enhanced abilities Thorn and Murtagh gained from Galbatorix' meddlings in their minds and bodies, they would still not be capable of killing Kulkarvek if he wakes up from his "slumber". It could be presumed that he was very powerful to pose such a great risk to them and because the Kull are the strongest group within Urgal society, it is presumed by most fans that Kulkarvek was a Kull. However, without further evidence, speculation on the matter proves fruitless.