It’s a bit awkward being an imaginary friend and not be adopted by a real child. Beekle in Dan Santat’s The Adventures of Beekle, The Unimaginary Friend, was born where imaginary friends come from, and like all the rest of them he waited for his human to claim him as their imaginary friend.
But nothing happened. Many of the others were found and went away to their children.
Beekle decided to take things into his own hands and sailed away from his imaginary world to the real world, which turned out to be nowhere near as exciting as he’d imagined. And still he didn’t find his child.
Eventually, though, as tends to happen in picture books, he did meet his real friend. They were awkward with each other until they got used to the thought of the other one, and then they became great friends, doing all those crazy things a child and its imaginary friend will do.