They never died. When Hogwarts was founded, the Founders decided to become immortal, a process lost in a particularly nasty witch trial (In which the witch in question survived trial by combat, trial by drowning, and lost to the trial by fire, books and scrolls burned with her)
In any case, Godric of Gryffindor, Helga of Hufflepuff, Rowena of Ravenclaw, and Salazar of Slytherin became close to immortal. But, to be as close to immortal as possible, they had to become animagi. They were reluctant, but with Merlin the first Dragon's help, they agreed to meet annually in a secluded area of the Forbidden Forest, so deep in only they knew where it lied.
The first time they transformed, they assumed that they would be their house animals. They were sorely mistaken.
Godric grew wings instead of a mane, and became Fawkes the Phoenix.
Helga grew rather than shrink in size, many times her own size, and became the helpful Giant Squid.
Rowena grew wings and talons, like an eagle, but a horse's body, and became the helpful Hippogriff Buckbeak.
Salazar, ever the snake, did become one, but was forced to live in the Chamber of Secrets as the basilisk.
When Harry Potter came to Hogwarts,Fawkes helped him in every way, even if it meant killing Slytherin, the murderer, and dying in the Battle of Hogwarts in the process. The Giant Squid made it her life's work to help him the Triwizard tournament (he certainly had it easier than Fleur), even though she was ripped to shreds by the merpeople. Buckbeak helped Sirius Black until he was killed, and then Rowena flew away to be haunted by Helena Ravenclaw until the hippogriff ended her life, to be with the other Founders's Four.
This short one-shot, in my opinion, is why those animals were so helpful, and why the founders weren't the House Ghosts.