Jackson Hole and Killer Kane are two different trails.
Jackson Hole is the trail you see from the top of Cliffhanger, down at the bottom of the cliff. You access it from the Chicken Corners trail, and it passes through private property at Camelot. It is a dead-end, "in-and-out" trail, and is not difficult.
Killer Kane (aka Minesweeper) is the dugway you see to your right as you head towards Hurrah Pass and Kane Creek. From the top of the trail, you actually look down on Hurrah Pass. It also passes through some private property (there is a gate), and is mostly on SITLA land. It is a fairly difficult trail, with a couple recent rock falls you need to climb over. The shelf road is very narrow and exposed. Along the way, there are several old mine shafts, one of which goes all the way through the mountain, and comes out the other side.
As far as I know, both are still open. I was on Killer Kane this past June, but I haven't been on Jackson Hole for probably 3-4 years.
Jeff