Firstly, what a wonderful job you’ve done in rescuing this little guy. Don’t give up on him yet. He is certainly not alone in exhibiting these symptoms!
You are correct in suspecting separation anxiety. The frantic frenzy to escape and find you or members of your family is perfectly understandable if we think about what’s happened to the little fella so far. Dogs are pack animals and in his short life he has already had to contend with being booted out of his original pack and although he is extremely grateful to have found your family, he can’t help but think that the same thing is going to happen again! So every time he’s left alone his anxiety levels go sky high with fears of being dumped or abandoned again. On top of all this, Border Collies are extremely active, highly intelligent dogs with a strong requirement for stimulating exercise.
My suggestions would be to first contact your local border collie club so that he can interact with dogs with similar needs and you can chat to owners of these dogs and perhaps pick up some tips. You need to tire this dog out and also mentally stimulate him so something like agility would be perfect to exercise his body and mind. Dogs are reassured by routine so try to keep things as regular as possible. Once he’s worked out that you always come back when he leaves he will be more settled but this will take work and perseverance. When you leave don’t make a fuss and ensure that he has a couple of mentally challenging toys such as the ones you fill with treats to occupy him while you’re gone. Leave the radio or TV on and when you return remain calm.
While he is learning to trust that he won’t be abandoned again (and maturing in age), you will need to ensure that he cannot escape from your property. Are you able to secure him in the house, perhaps in the laundry or a garage? If this is not possible, I would strongly recommend having a professionally built dog run erected in the backyard. Unfortunately, leaving this little guy loose in your backyard is going to result in continued escaping and at worst a road fatality so a temporary alternative would go a long way towards reducing your concern for his safety.Lastly, he will improve – I promise! But it will take time and application of the above tips. The rewards however will be tremendous as border collies make fantastic pets with correct training. Hang in there and good luck!