Hi I have a rescue border collie and thought I would share my experience.
We were told our dog was house trained, good with people although a little nervous around men, good in the car, ignored cats (we have one) and various other things.
We had him last year and I honestly thought I would have a nervous breakdown, he chased the cat, clearly had never been in a house (took us over half an hour to get him through a door), we would not get him in the car for 6 months, he was nervous around everyone and totally destructive. I posted on this board for advice and contacted the rescue who totally washed their hands of him. Within two months he had eaten my settee, tables, destroyed my kitchen and lots of other things such as shoes, etc.
For 6 months I could not sit down at night as he started pawing me to the point he ripped several items of clothes. He was not aggressive but I could not work out what he wanted.
I tried lots of training, behaviourists, etc and nothing worked.
Fast forward to 12 months on and I love the bones of my dog. He can be left without destroying anything (touch wood), loves the car, likes to snuggle at night, enjoys a walk, plays with the cat and is getting better with men. I am so glad I perservered and I still to this day do not know what made him settle although I give a lot of credit to positive rewarding as this is when mine turned a corner I think!!
It can and does get better and I genuinely thought more than once that I would have to rehome, I am so glad I did not .