Well... mostly alone. In addition to the Ruby Claw sitting on a pressure plate atop the altar in the middle of the room, three of the corpses here are draugr that will rise to attack you when you take possession of the claw. You can most likely locate and slay them with little trouble before taking the claw, which is advisable since you can begin dealing with them before they’ve awoken, where taking the claw gives them all time to rise up.
Check throughout the room for several burial urns and a coin purse, and make sure to look behind the iron door off to the left and pick up a spare weapon and a potion from the room beyond. Make sure you’ve taken everything of value from the corpses here as well, and then move on through the porticullis at the back of the room, which opens when you remove the Ruby Claw from its pressure-plate stand.
The hallway behind the porticullis quickly takes a turn to the right, and as soon as you look down the hallway you’ll spot the ghost again, heading off to the left at the T-intersection ahead of you. Mind your step as you try to catch up, for there is a pressure plate just before the end of the hallway that will leave you skewered on several spears from the walls if you aren’t careful.
Following this, the hallway to the left goes down some stairs, then continues descending while turning to the right. In one of the corners as you descend is a small table, which holds a couple of burnt books, an untouchable skull, and a pair of soul gems. At the end of the downward helix, you will come to what appears to be a stone wall. If you look off to the right, though, you can spot a ring-chain. Pulling this will cause the wall to slide open, revealing a set of the small, circular burial chambers so frequently seen in Nord ruins. You will also see the ghost again, turning and walking directly away from you into (and through) another apparent stone wall.
Take care in this area, for there are frostvenom spiders here. It’s fairly easy to attract a single small one with little risk- just put a few arrows into that far wall, and the spider will emerge from the left side of the far chamber. To find the other spider, head to that same chamber and look in the direction it emerged from. You will find more round rooms there, with the other spider idling in and patrolling the farthest of these.
Once both spiders are dead, head to where the second one was lurking and destroy the web on the wall to uncover a locked chest with some minor treasures in it. Similarly, rip the webs free of the wall in the first dark chamber and you can find a somewhat rare weapon. Finally, check the last of the four dark chambers. You will notice that there is a pull-chain near the section of wall where you might have expected to find a passage back to the first of the round burial chambers.