Galaxies die from the inside out
Star formation in what are now "dead" galaxies sputtered out billions of years ago. ESO's Very Large Telescope and the NASA/ESA Hubble Space Telescope have revealed that three billion years after the Big Bang, these galaxies still made stars on their outskirts, but no longer in their interiors. The quenching of star formation seems to have started in the cores of the galaxies and then spread to the outer parts.
This diagram illustrates this process. Galaxies in the early Universe appear at the left. The blue regions are where star formation is in progress and the red regions are the "dead" regions where only older redder stars remain and there are no more young blue stars being formed. The resulting giant spheroidal galaxies in the modern Universe appear on the right.