Originally Posted by Psyduck

It's not that Dumbledore was unconcerned. He just said that it was beyond help.

I'm back to my original impression -- that it was Voldemort's last shard. He and Harry were both knocked out for a minute, and I think that both were in that limbo place -- a kind of near-death, out-of-body experience.
Harry, with his soul intact and as pure as the driven snow, was able to form the place as he liked and was able to have a conversation with Dumbledore. Voldemort's soul was so damaged and evil that it could do nothing but whimper.