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Dumbledore left Ron the Deluminator, which turns out to be a way for Ron to find his friends after he runs away.
Did Dumbledore suspects such a case (so that's why he gave it to Ron)?
I remember reading something about this matter, possibly in the books.
Yes, the book said something to that effect (See @DavidS's answer for the quote) so you're remembering correctly.
BUT, that was just Ron's personal guess and not necessarily the "truth" in-universe, so in my opinion that doesn't directly answer the question.
However, we do have the Word of God confirmation that he did indeed know something in general about Ron needing "guidance"[1].
Sampotterish: Why did dumbledore want ron to keep his deluminator
J.K. Rowling: Because he knew that Ron might need a little more guidance than the other two.
J.K. Rowling: Dumbledore understood Ron's importance in the trio. He wasn't the most skilled, or the most intelligent, but he held them together; his humour and his good heart were essential.
(J.K. Rowling and the Live Chat, Bloomsbury.com, July 30, 2007 (2.00-3.00pm BST).)
[1] ... which leads me to believe that Deluminator may have had other possible uses depending on what Ron's specific need for guidance would have been. But that's just a personal guess with no canon backup
This is the passage in question:
“[Dumbledore] knew what he was doing when he gave me the Deluminator, didn’t he? He – well,” Ron’s ears turned bright red and he became engrossed in a tuft of grass at his feet, which he prodded with his toe, “he must’ve known I’d run out on you.”
“No,” Harry corrected him. “He must’ve always known you’d always want to come back.”
— Deathly Hallows, chapter 20 (Xenophilius Lovegood)
