What happens when someone dies? Who keeps the bitcoins?
If he didn't left to anyone his private key, will the bitcoins be lost forever and ever?
Yes, those coins would be lost.  It would be as if you buried a chest of gold out in the middle of nowhere and died without telling anyone about it.

Though it is possible (though mindbendingly unlikely.  Even if bitcoin keeps existing until the heat death of the universe, it will almost certainly never happen.) for someone to randomly recreate the keypair for those coins and thus take possession of them.