If quasars are supermassive black holes at the center of young galaxies what happens to them? How could they disappear?
Quasars are very distant young galaxies seen as they were billions of years ago.
Quasars are powered by matter falling into supermassive black holes. The only galaxies with enough material to power a quasar are young galaxies and galaxies which have collided.
The quasars which have been detected are billions of light years away. They are young galaxies created in the early times of the universe and their light is only just reaching us.
When the material falling into the supermassive black hole is depleted, the reverts to a normal, active galaxy. All of the observed distant quasars will have ceased to be quasars billions of years ago.
Our Milky Way galaxy is going to collide with the Andromeda galaxy. When that happens, enough material could be available near one or both of the galaxy's supermassive black holes to start a quasar. If it happens, the quasar will exist until the material is depleted.