Hi!
Just wanted to let everyone know, who may have been wondering, that Max is fine. He finally broke the end of the claw off that was loose, and he's running around enjoying life as usual. He knew what he was doing all along!
I would recommend people see the vet anyway if this happens to their dog since it would have been difficult for me to clip the broken part of the claw off myself... which was all that was required in this case.