Adopted dog destroying house when alone. Anxiety or boredom? Crate?

Destructive behavior like this when you're not home is usually caused by separation anxiety - some dogs will chew things when they're bored, but if there is significant destruction and it only happens when you're gone, anxiety is much more likely. If you want to know for sure, I would suggest videotaping her the next time you go out - it's usually very easy to see on the video if this is anxiety vs. boredom.

There are a few things you can do to try and help her. You can try crating her, but be aware that many dogs with this problem are more anxious when they are confined - she won't be able to do as much damage to your home, but she may injure herself if she panics trying to escape. I would strongly recommend leaving her with a special long-lasting treat of some kind every time you leave the house, like a Kong toy stuffed with peanut butter or something similar. You may also want to try a DAP pheromone collar along with a natural calming supplement like Composure or Zylkene to help decrease her anxiety.

If you don't see improvement within the next 1-2 weeks, you should talk with your vet about the problem as she may need prescription medication to treat her anxiety, at least for a while. You could also request referral to a veterinary behaviorist for additional help if the problem is severe.