dead stars are ultra-dense, almost pure balls of Iron.
That depends on the type of death a star suffers.
If the star is low mass, after it expands into a giant, it can blow away its atmosphere. The core would remain - a white dwarf. Not all stars can reach temperatures capable of fusing iron. Many of them are composed of mainly Carbon and Oxygen and can maintain fusion of hot enough.
In such a star, the main component of pressure is provided by electron pressure.
If the star gains mass (through accretion), the electrons would need to move faster than the speed of light to hold up against gravity. Since that's impossible, the star collapses. That happens at 1.38 solar masses (Chandrasekhar limit) and results in a type Ia supernova.
Since this always happens at approximately 1.38 solar masses and all white dwarfs have approximately the same density, the energy released in this type of supernova is always approximately the same - they gained a nickname "standard candle".
In the collapse, protons and electrons can fuse, creating neutrons. After the collapse, the more heavy neutrons can provide sufficient pressure to hold the star up against gravity. Since they're heavier, they can move at slower speeds to provide enough pressure.
For a collapse of a neutron star into a black hole, the estimate is given as 3 to 4 solar masses, however, no neutron star heavier than 2 solar masses has so far been found.
Just wanted to set things straight...