Considering a bijuu is nothing more than a concentrated mass of chakra, they can't physically die. When the Jinchuuriki dies, and there is no other person available to take over as Jinchuuriki, the bijuu either disappears together with his host or breaks free and causes destruction before it's sealed again.
In the case of disappearing with the host, the bijuu will after a certain time appear freely on the earth again and cause destruction until it's sealed. That's why they always make sure they have another person available to take over as Jinchuuriki because the destruction would be too great if a bijuu is left free.
So a bijuu doesn't die, it just disappears for a while before it reappears again.