I've read some posts on here related to this topic, but all of the tricks have already been used.
TL;DR: My mum rescued an abused pup with head trauma.
My mother has a rescue pup. He belonged to a neighbour for his first few months of life, and bonded with my mum over that period of time (neighbours didn't show him much love). She was (and still is) the owner of the pup's sister. The neighbour gave him away to a local mechanic who, we believe, severely abused him. He's terrified of men now, and winces if you move too fast near him. Based on his sudden seizures when she found and adopted him from a local rescue (he was found on the streets after being abandoned by the mechanic), we believe he had severe head trauma from the abuse.
He's a very good dog, but now he won't leave her alone.
If she heads to the bathroom, he's going too. If she goes to do laundry, he's coming. He is at her side non-stop, and if she ever dares to leave the house he will scream his face off. Even if she's just standing on the other side of a baby gate he will flip out. She owns two other dogs, one being his sister and the other being an elderly dog. She also owns a rabbit, and a cat, and millions of fun mind-game dog toys.
She has tried making her leaving the house a good experience with positive reinforcement. She has tried "calming dog music". She has tried leaving other people at home with him. She has tried puzzle toys. She has tried crating. She has tried absolutely everything with this boy.
The clingy behaviour is annoying, yes, but that's not even the biggest issue here. His seizures are, and they are caused by stress. He's on medication for it, but if he gets too stressed he will still have an epileptic episode.
If he isn't by her side all constantly, there's a very good chance he'll have a seizure - and could very likely die. Every seizure is one step closer to him possibly passing away, and there seems to be nothing she can do except just stay at home with him 24/7.