Pulsars are really a sub-class of neutron stars.
Such stars have exhausted their nuclear fuel, and can no longer produce enough heat to balance the intense gravity. That star would have been very bright, like Rigel, for instance. After the nuclear engine in the stellar core has used up all the hydrogen it could find, the core collapses until it is sufficiently dense to fuse helium into carbon and oxygen, then silicon, and so on, until the only available reactions left involve burning iron, which requires more energy than it produces. At this point, there is no nuclear energy left in the stellar core, and the core collapses under its own weight. The gravity in massive stars, however, is so strong that the electron shells collapse, and inverse beta decays begin, as atomic nuclei swallow their electrons.