As the following examples show, if Y possesses X we can use the double possessive "X of Y's".
an example from merriam-webster.com:
(1) It had long been a dream of Mabel's to win the baking contest.
That is: Mabel possesses a dream.
an example from the textbook "The Oxford Dictionary of English Grammar", page 178:
(2) some books of Jane’s
That is: Jane possesses some books.
an example from an answer on english.stackexchange.com:
(3) that dog of John's
That is: John possesses that dog.
But in a comment on ell.stackexchange.com, I was told that the following phrase is incorrect:
(4) a car of my friend's
Although the sense is the same: my friend possesses a car.
So why is "(4)" incorrect, whereas (1), (2) & (3) are correct?