The area contains a puzzle door that requires the coral dragon claw to open, which can be found either from Birna in Winterhold or within the barrow itself, located on a pedestal past a puzzle room. If one obtains the quest to retrieve the Helm of Winterhold from this destination before talking to Birna and obtaining the coral dragon claw from her, and instead obtain the claw from within the barrow, then one can still return to Birna and receive the second claw for a modest price. However, that will not start a second quest, and returning to the barrow at that point shows things are exactly as they were left.
I passed the puzzle room with the snake in the grass, whale in the water, and eagle in the sun thingy.
This is the pedestal
I didn't get the claw from Birna so I should get that from that pedestal right? No.
I met Birna, and no coral dragonstone from her either :(