The old phrase "down to the lick log," means you're close to the end of negotiations, nearing some kind of decision, or your situation is about to change.
To cattle, the phrase sometimes relates to the second to the last thing they do before they die.
It was an old rancher trick to take them to the salt lick and then to water, increasing their weight before slaughter.
Some older layers use this term when referring to having exhausted all settlement efforts before they go to trial, leaving only the trial, dismissal, or some other 'final' resolution/end to the case. Everything has been done that could/should be done to resolve the matter, now it is time to resolve it. - A Little Gossip

So, having come to the 'lick.log' for Cades Cove as a community, we find that no homes are now owned by the residents.