Kaurik used to be a village bang on the border with Tibet ! Kaurik is still used on milestones along NH 22. It can be easily located on google maps. Kaurik is a mysterious place which was deserted some 25-28 years back in earthquake/flash floods and now you can find ruins of the place if you are ready to hike a bit once the road ends after about 19 KMs. Hoorling village has the largest number of survivors from Kaurik village.
Beyond Kaurik, there is a village called Lepcha which requires you to further hike about an hour or so. Lepcha is the last place in India you can reach and ahead lies Tibet beyond the Indo-Tibet Border ends. Anyhow, Kaurik falls under a restricted area as far as I know and permits are hard to find for Kaurik. The entire area is under ITBP control.
So, the best bet is to land there and ask the permissions from army guys if you can pass through. If they say yes, then go ahead and explore this amazing mysterious place in Spiti Valley.