Seperation anxiety is a very common problem. Unfortunatly its more or less managed , than it is solved. I have a dach with a mild case of it, he too is a rescue.
What we were told to do is, never make a big deal out of leaving "saying good bye to pup", going thru some big giant ritual when leaving", and never make a big deal when you come home either. Basically , put dog up a while before you leave, so she can see you walking around, and being "there" while she is in her "goodbye place"....and when you come home , IGNORE her for a little while as well.
This usually helps the dog with its "anxiety" , which is not a behavor problem as most people think. It actuall IS a mental issue that the dog really cannot help itself.
I found our urinating problem was solved by diapering pup only while gone. (be careful not to put on just as you are leaving, or this is also a SIGNAL to pup). we just put ours on about 20 mins or so before we leave.
There is also some pharamone plug in things that you can get that help "soothe" the pup while you are gone. Some can be expensive, but it beats having to rewalpaper your laundry room, or get a new door, or the VET bill from pup hurting itself.
Have your friend GOOGLE "canine seperation anxiety" . there are MANY non medication routes to try first.
Our dach has to be in a kennel in another room all night because left out he destroys things, and in it he howls , barks and whines all night.
He is learning slowly bedtime, and morning routines, so he is not quite as noisy or destructive. SO THERE IS HOPE!
and there is no way to know if she was "seperation anxiety ridden" before her rescue, or if being rescued triggered it.
(unless they contact the owner and ask i guess).
Often if its just triggered BY rescueing...it can quite down with routine and time.
If it was just born with it...its harder.
Thats about all i got.